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About 10,000 papers for “Bounded operator”
Salim D. M, Ahmed M.K. · journal of the college of basic education · 2023
In this paper, we give the general solutions of bounded operator equation (1) , where and are noninvertible operator .on complex Hilbert space and properties of the mapping
Cited by 0Open access
Arnold Lebow · The Michigan Mathematical Journal · 1968
Cited by 37Open access
O. V. Kužel′ · Translations - American Mathematical Society/Translations · 1970
Cited by 3
D. Benjamin Mathes · Proceedings of the American Mathematical Society · 1989
In this paper it is shown that the set of invariant operator ranges that induce completely bounded homomorphisms is a sublattice of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L a t Subscript 1 slash 2 Baseline German upper A"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>Lat</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>1</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo><!-- --></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">A</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\operatorname {Lat}_{1/2}\mathfrak {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, when <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper A"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">A</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is any norm closed algebra of operators on a Hilbert space. A characterization of this sublattice is given, and several concrete examples are discussed.
Cited by 0Open access
Evseev, Nikita · arXiv (Cornell University) · 2017
We study a composition operator on Lorentz spaces. In particular we provide necessary and sufficient conditions under which a measurable mapping induces a bounded composition operator.
Cited by 0Open access
Alvaro Arias · Proceedings of the American Mathematical Society · 1996
In this paper the author proves that any two elements from one of the following classes of operators are completely isomorphic to each other. $\{VN(F_{n}):n\geq 2\}$. The $II_{1}$ factors generated by the left regular representation of the free group on $n$-generators. $\{C_{\lambda }^{*}(F_{n}):n\geq 2\}$. The reduced $C^{*}$-algebras of the free group on $n$-generators. Some ânon-commutativeâ analytic spaces introduced by G. Popescu in 1991. The paper ends with some applications to Popescuâs version of von Neumannâs inequality.
Cited by 3Open access
N. A. Evseev · Mathematical Notes · 2017
We study composition operators on Lorentz spaces. In particular, we obtain necessary and sufficient conditions under which a measurable mapping induces a bounded composition operator.
Cited by 1Open access
K. P. Deepesha, S. H. Kulkarnib, M. T. Nairc · 2016
Abstract. Let T be a densely defined closed operator between Banach spaces X and Y. A concept of approx-imation numbers, called T–approximation numbers, is considered for T–bounded operators between Banach spaces X and Z with their domains contained in X, and some properties of such T–approximation numbers are studied. The theorems proved in the paper include a result on approximation of T–approximation num-bers of a T–bounded operator A using T–approximation numbers of An, where {An} is a certain sequence of operators which converges to A in some sense. This result is analogous to a theorem proved recently by the authors in [3] for bounded linear operators. 1.
Cited by 0
Seán Dineen, Cristina Radu · MATHEMATICA SCANDINAVICA · 2010
In this article we introduce the concept of a completely bounded polynomial between operator spaces, prove some basic properties and determine the operator structure of the space of diagonal polynomials on the more important operator Hilbert spaces.
Cited by 3Open access
Vern I. Paulsen · Proceedings of the American Mathematical Society · 1984
Let <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> be a unital operator algebra. We prove that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="rho"> <mml:semantics> <mml:mi>ρ</mml:mi> <mml:annotation encoding="application/x-tex">\rho</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a completely bounded, unital homomorphism of <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> into the algebra of bounded operators on a Hilbert space, then there exists a similarity <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S"> <mml:semantics> <mml:mi>S</mml:mi> <mml:annotation encoding="application/x-tex">S</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, with <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar upper S Superscript negative 1 Baseline double-vertical-bar dot double-vertical-bar upper S double-vertical-bar equals double-vertical-bar rho double-vertical-bar Subscript c b"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo symmetric="true">‖</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>S</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> <mml:mo symmetric="true">‖</mml:mo> </mml:mrow> <mml:mo>⋅</mml:mo> <mml:mrow> <mml:mo symmetric="true">‖</mml:mo> <mml:mi>S</mml:mi> <mml:mo symmetric="true">‖</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow> <mml:mo symmetric="true">‖</mml:mo> <mml:mi>ρ</mml:mi> <mml:mo symmetric="true">‖</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>c</mml:mi> <mml:mi>b</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\left \| {{S^{ - 1}}} \right \| \cdot \left \| S \right \| = {\left \| \rho \right \|_{cb}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, such that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S Superscript negative 1 Baseline rho left-parenthesis dot right-parenthesis upper S"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>S</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mi>ρ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mo>⋅</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mi>S</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">{S^{ - 1}}\rho ( \cdot )S</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a completely contractive homomorphism. We also show how Rota’s theorem on operators similar to contractions and the result of Sz.-Nagy and Foias on the similarity of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="rho"> <mml:semantics> <mml:mi>ρ</mml:mi> <mml:annotation encoding="application/x-tex">\rho</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dilations to contractions can be deduced from this result.
Cited by 41
Vern I. Paulsen · Proceedings of the American Mathematical Society · 1984
Let A be a unital operator algebra.We prove that if p is a completely bounded, unital homomorphism of A into the algebra of bounded operators on a Hubert space, then there exists a similarity S, with ||S-1|| ||S|| = ||p||cb, such that S_1p(-)S is a completely contractive homomorphism.We also show how Rota's theorem on operators similar to contractions and the result of Sz.-Nagy and Foias on the similarity of p-dilations to contractions can be deduced from this result.
Cited by 10Open access
D. Benjamin Mathes · Proceedings of the American Mathematical Society · 1989
In this paper it is shown that the set of invariant operator ranges that induce completely bounded homomorphisms is a sublattice of $\operatorname {Lat}_{1/2}\mathfrak {A}$, when $\mathfrak {A}$ is any norm closed algebra of operators on a Hilbert space. A characterization of this sublattice is given, and several concrete examples are discussed.
Cited by 0
Jiankui Li, Zhidong Pan · 2015
Abstract. We introduce a concept “bounded reflexivity ” for a subspace of operators on a normed space. We explore the properties of bounded reflexiv-ity, study the similarities and differences between bounded reflexivity and the usual reflexivity for a subspace of operators. As applications of bounded re-flexivity, we give alternative proofs of some well known results about positivity and complete positivity of elementary operators.
Cited by 0
Manar Naji Ghayyib, Jehad R. Kider · Baghdad Science Journal · 2021
Our goal in the present paper is to recall the concept of general fuzzy normed space and its basic properties in order to define the adjoint operator of a general fuzzy bounded operator from a general fuzzy normed space V into another general fuzzy normed space U. After that basic properties of the adjoint operator were proved then the definition of fuzzy reflexive general fuzzy normed space was introduced in order to prove that every finite dimensional general fuzzy normed space is fuzzy reflexive.
Cited by 6Open access
Hamed Najafi, Mohammad Sal Moslehian, Masatoshi Fujii et al. · Hokkaido Mathematical Journal · 2016
Recently the behavior of operator monotone functions on unbounded intervals with respect to the relation of strictly positivity has been investigated. In this paper we deeply study such behavior not only for operator monotone functions but also for operator convex functions on bounded intervals. More precisely, we prove that if $f$ is a nonlinear operator convex function on a bounded interval $(a,b)$ and $A, B$ are bounded linear operators acting on a Hilbert space with spectra in $(a,b)$ and $A-B$ is invertible, then $sf(A)+(1-s)f(B)>f(sA+(1-s)B)$. A short proof for a similar known result concerning a nonconstant operator monotone function on $[0,\infty)$ is presented. Another purpose is to find a lower bound for $f(A)-f(B)$, where $f$ is a nonconstant operator monotone function, by using a key lemma. We also give an estimation of the Furuta inequality, which is an excellent extension of the L\"owner--Heinz inequality.
Cited by 3
Hayder S. Mohammed, Али А. Шукур · AIP conference proceedings · 2025
Cited by 0
Ben Mathes · Journal of Functional Analysis · 1991
Cited by 1
Nathanial P. Brown, Narutaka Ozawa · Graduate studies in mathematics · 2008
Cited by 0
René Erlín Castillo, Humberto Rafeiro, Eduard Trousselot · SHILAP Revista de lepidopterología · 2014
"In this paper we show that if the Nemytskii operator maps the (φ, α)-bounded variation space into itself and satisfies some Lipschitz condi- tion, then there are two functions g and h belonging to the (φ, α)-bounded variation space such that f (t, y) = g(t)y + h(t) for all t ∈ [a, b], y ∈ R."
Cited by 2Open access
Özlem Bakşi, Ehliman Adıgüzelov · 2004
Cited by 0