Takeshi Miura · Contemporary mathematics - American Mathematical Society · 2015
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a compact Hausdorff space. We denote by <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">C(X)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> the Banach space of all continuous complex valued functions on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with respect to the supremum norm. A function space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding="application/x-tex">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a normed linear subspace of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">C(X)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> that contains the constant function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="1"> <mml:semantics> <mml:mn>1</mml:mn> <mml:annotation encoding="application/x-tex">1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and separates the points of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . We give a necessary and sufficient condition for a surjective distance preserving map between two function spaces be represented by a weighted composition operator.
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Sun Ning, Yang Zaifu · Yokohama National University Repository (Yokohama National University) · 2016
Given the unit sphere S^n, we prove the following theorem and several extensions: For any continuous function f:S^n $\\mapsto$ S^n, if f has no fixed point or if f has no antifixed point in S^n, then f is surjective and has a point x^* $\\in$ S^n such that f(x^*) = -f(-x^*). We also apply this result to a competitive exchange economy and demonstrate the existence of an equilibrium in the economy.
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Michael Wüstner · 2001
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Cabrera-Padilla, M. G., Jim\'enez-Vargas, A., Miura, Takeshi et al. · ArXiv.org · 2025
Let $A$ be a complex Banach space with a norm $\|f\|=\|f\|_X+\|d(f)\|_Y$ for $f\in A$, where $d$ is a complex linear map from $A$ onto a Banach space $B$, and $\|\cdot\|_K$ represents the supremum norm on a compact Hausdorff space $K$. In this paper, we characterize surjective isometries on $(A,\|\cdot\|)$, which may be nonlinear. This unifies former results on surjective isometries between specific function spaces.
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Cabrera-Padilla, M. G., Jiménez-Vargas, A., Miura, Takeshi et al. · arXiv (Cornell University) · 2025
Let $A$ be a complex Banach space with a norm $\|f\|=\|f\|_X+\|d(f)\|_Y$ for $f\in A$, where $d$ is a complex linear map from $A$ onto a Banach space $B$, and $\|\cdot\|_K$ represents the supremum norm on a compact Hausdorff space $K$. In this paper, we characterize surjective isometries on $(A,\|\cdot\|)$, which may be nonlinear. This unifies former results on surjective isometries between specific function spaces.
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Karl H. Hofmann, Wolfgang Ruppert · Memoirs of the American Mathematical Society · 1997
Introduction The basic theory of exponential semigroups in Lie groups Weyl groups and finiteness properties of Cartan subalgebras Lie semialgebras More examples Test algebras and groups Groups supporting reduced weakly exponential semigroups Roots and root spaces Appendix: The hyperspace of a locally compact space References Index.
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Fernanda Botelho, James Jamison · Contemporary mathematics - American Mathematical Society · 2017
In this paper we give a representation for the surjective and linear isometries on spaces of vector valued absolutely continuous functions with <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -integrable derivatives ( <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="1 greater-than p greater-than normal infinity"> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>></mml:mo> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mi mathvariant="normal"> ∞ </mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">1>p> \infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula> ). The range space is a Banach space which is smooth, reflexive and separable. Representations for the generalized bi-circular projections and the bounded hermitian operators are also derived.
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Lei Li, Risheng Wang · Journal of Mathematical Analysis and Applications · 2015
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M. Wuestner · Journal of Lie theory · 1995
We discuss the example of a complex simple Lie group G, with trivial center, whose exponential map is not surjective and with dim C G = 10.
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Youngik Lee · arXiv (Cornell University) · 2019
This research focuses on the possibility of the surjective relation between\nsymmetric potential function and its scattering matrix in 1-dimension. The\ntheory bases on the property of wave function symmetry and boundary conditions.\nThis research shows the surjective relation in some particular cases, delta\nfunction potential, and finite square wall potential, and disproves the\ninjective relation of the arbitrary potential function and its S-matrix.\n
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Communicated M. Moskowitz · 2012
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María Cueto-Avellaneda, Daisuke Hirota, Takeshi Miura et al. · Quaestiones Mathematicae · 2022
In this note we present two new positive answers to Tingley’s problem in certain subspaces of function algebras. In the first result we prove that every surjective isometry between the unit spheres, S(A) and S(B), of two uniformly closed function algebras A and B on locally compact Hausdorff spaces can be extended to a surjective real linear isometry from A onto B. In a second part we study surjective isometries between the unit spheres of two abelian JB*-triples represented as spaces of continuous functions of the formwhere X is a (locally compact Hausdorff) principal -bundle and denotes the unit sphere of ℂ. We establish that every surjective isometry admits an extension to a surjective real linear isometry between these two abelian JB*-triples.
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Osamu Hatori, Shiho Oi · Contemporary mathematics - American Mathematical Society · 2019
We study 2-local reflexivity of the set of all surjective isometries between certain function spaces. We do not assume linearity for isometries. We prove that a 2-local isometry in the group of all surjective isometries on the algebra of all continuously differentiable functions on the closed unit interval with respect to several norms is a surjective isometry. We also prove that a 2-local isometry in the group of all surjective isometries on the Banach algebra of all Lipschitz functions on the closed unit interval with the sum-norm is a surjective isometry.
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Anne Fernengel, Peter Koepke · arXiv (Cornell University) · 2013
By Easton's theorem one can force the exponential function on regular cardinals to take rather arbitrary cardinal values provided monotonicity and Koenig's lemma are respected. In models without choice we employ a "surjective" version of the exponential function. We then prove a choiceless Easton's theorem: one can force the surjective exponential function on all infinite cardinals to take arbitrary cardinal values, provided monotonicity and Cantor's theorem are satisfied, irrespective of cofinalities.
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C Buse, Donal 'Regan, Olivia Saierli · Operators and Matrices · 2021
Let P be a complex polynomial. We prove that the associated polynomial matrixvalued function P is surjective if for each C the polynomial P - has at least a simple zero and it is not surjective if it does not have the double zero property.
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Николай Тарханов · Medical Entomology and Zoology · 1995
Function spaces pseudodifferential operators in the spaces of distributions on closed sets capacity systems of differential equations with injective (surjective) symbol coarse results on approximation by solutions of a system with surjective symbol approximation in spaces of smooth functions approximation in spaces of Holder functions approximation in spaces of Sobolev functions generalized boundary values of solutions of a system with injective symbol. (Part contents).
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Peter Fulla, Hannes Uppman, Stanislav Živný · ACM Transactions on Computation Theory · 2018
Valued constraint satisfaction problems (VCSPs) are discrete optimisation problems with a (Q ∪ {∞ })-valued objective function given as a sum of fixed-arity functions. In Boolean surjective VCSPs, variables take on labels from D = {0,1}, and an optimal assignment is required to use both labels from D . Examples include the classical global Min-Cut problem in graphs and the Minimum Distance problem studied in coding theory. We establish a dichotomy theorem and thus give a complete complexity classification of Boolean surjective VCSPs with respect to exact solvability. Our work generalises the dichotomy for {0, ∞}-valued constraint languages (corresponding to surjective decision CSPs) obtained by Creignou and Hébrard. For the maximisation problem of Q ≥0 -valued surjective VCSPs, we also establish a dichotomy theorem with respect to approximability. Unlike in the case of Boolean surjective (decision) CSPs, there appears a novel tractable class of languages that is trivial in the non-surjective setting. This newly discovered tractable class has an interesting mathematical structure related to downsets and upsets. Our main contribution is identifying this class and proving that it lies on the borderline of tractability. A crucial part of our proof is a polynomial-time algorithm for enumerating all near-optimal solutions to a generalised Min-Cut problem, which might be of independent interest.
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M Zaidenberg · arXiv (Cornell University) · 1995
The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.
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González-Anaya, Javier, Nasserden, Brett, Zotine, Sasha · ArXiv.org · 2025
We study surjective endomorphisms of projective bundles over toric varieties, achieving three main results. First, we provide a structural theorem describing endomorphisms of projectivized split bundles over arbitrary base varieties, which we use to classify all surjective endomorphisms of Hirzebruch surfaces and construct novel families of examples. Second, for non-split equivariant bundles over toric varieties, we prove that the dynamical degree of an endomorphism of the projectivization is controlled by the base morphism; as a consequence, we establish the Kawaguchi--Silverman conjecture for such bundles. Third, using an explicit transition function method, we prove that projectivizations of tangent and cotangent bundles of smooth toric varieties admit no non-automorphic surjective endomorphisms commuting with toric morphisms on the base.
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A.A. Alimov, V.I. Chilin · Владикавказский математический журнал · 2019
Let mathcal M be a von Neumann algebra equipped with a faithful normal finite trace tau, and let Sleft( mathcalM, tauright) be an ast -algebra of all tau -measurable operators affiliated with mathcal M . For x in Sleft( mathcalM, tauright) the generalized singular value function mu(x):trightarrow mu(tx), t0, is defined by the equality mu(tx)infxp_mathcalM:, p2pp in mathcalM, , tau(mathbf1-p)leq t. Let psi be an increasing concave continuous function on 0, infty) with psi(0) 0, psi(infty)infty, and let Lambda_psi(mathcal M,tau) left x in Sleft( mathcalM, tauright): x _psi int_0inftymu(tx)dpsi(t) infty right be the non-commutative Lorentz space. A surjective (not necessarily linear) mapping V:, Lambda_psi(mathcal M,tau) to Lambda_psi(mathcal M,tau) is called a surjective 2-local isometry, if for any x, y in Lambda_psi(mathcal M,tau) there exists a surjective linear isometry V_x, y:, Lambda_psi(mathcal M,tau) to Lambda_psi(mathcal M,tau) such that V(x) V_x, y(x) and V(y) V_x, y(y). It is proved that in the case when mathcalM is a factor, every surjective 2-local isometry V:Lambda_psi(mathcal M,tau) to Lambda_psi(mathcal M,tau) is a linear isometry.
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