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About 10,000 papers for “operators”

Operators Approximable by Hypercyclic Operators

James Boland · Mathematical Proceedings of the Royal Irish Academy · 2015

We show that operators on a separable infinite dimensional Banach space $X$ of the form $I +S$, where $S$ is an operator with dense generalised kernel, must lie in the norm closure of the hypercyclic operators on $X$, in fact in the closure of the mixing operators.

Cited by 0Open access

Nuclear operators and compact operators.

Holman Alejandro Perez Ayala · Universidad Industrial de Santander · 2017

En 1955 el matemático Alexander Grothendieck introduce los operadores nucleares en su artículo Produits tensoriels topologiques et espaces nucléaires, con el fin de generalizar los operadores de clase-trazo definidos en espacios de Hilbert. Una serie de trabajos a partir de entonces centraron su atención en el estudio de los operadores nucleares definidos en espacios de funciones. Este trabajo consiste en estudiar algunos conceptos y definiciones sobre operadores nucleares relacionandolos con la teoría de operadores compactos. En el primer capítulo se abordarán algunos resultados previos necesarios en el desarrollo del proyecto en capítulos posteriores, por ejemplo teoremas fundamentales sobre operadores compactos, forma polar de un operador y la integral de Bocnher. En el segundo capítulo se definirá el concepto de operador nuclear y de norma nuclear, se presentan y demuestran una serie de teoremas que muestran la relación existente entre los operadores nucleares y los operadores compactos y se estudian los operadores nucleares en espacios de Hilbert. En el tercer capítulo se establece la teoría necesaria para la demostración del teorema principal, el cual es la no existencia de un isomorfismo entre el espacio N (C(Q)) (espacio de operadores nucleares sobre C(Q)) y un subespacio de K(C(Q′ )) (espacio de operadores compactos sobre C(Q′ )), siendo Q y Q′ espacios métricos compactos y numerables.

Cited by 0Open access

Toeplitz operators and localization operators

Miroslav Engliš · Transactions of the American Mathematical Society · 2008

We show that for any localization operator on the Fock space with polynomial window, there exists a constant coefficient linear partial differential operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding="application/x-tex">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that the localization operator with symbol <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding="application/x-tex">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> coincides with the Toeplitz operator with symbol <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D f"> <mml:semantics> <mml:mrow> <mml:mi>D</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">Df</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . An analogous result also holds in the context of Bergman spaces on bounded symmetric domains. This verifies a recent conjecture of Coburn and simplifies and generalizes recent results of Lo.

Cited by 27Open access

Operators Commuting with Positive Operators

M. Radjabalipour · Proceedings of the American Mathematical Society · 1979

Necessary and sufficient conditions are obtained for an operator to commute with a positive operator.

Cited by 4Open access

Toeplitz Operators and Hankel Operators

李绍宽 · Acta Scientiarum Naturalium Universitatis Sunyatseni · 1993

In Ref. it is proved that for Toeplitz operator T_φ and Hankel operator H_ψ on Hardy space H~2(T) if R(T_φ)R(H_ψ), then T_φ=0. In this note we will discuss similar problem for the Toeplitz operators and Hankel operators related with the shifts. The result extended not only to the general case, but also to the Beurling problem.

Cited by 0

Aleksandrov operators as smoothing operators

Alec Matheson · Illinois Journal of Mathematics · 2001

A holomorphic function $b$ mapping the unit disk $\disk$ into itself induces a family of measures $\tau_\alpha$, $|\alpha|=1$, on the unit circle $\circle$ by means of Herglotz's Theorem. This family of measures defines the Aleksandrov operator $A_b$ by means of the formula $A_b f(\alpha) = \int_\circle f(\zeta)\,d\tau_\alpha(\zeta)$, at least for continuous $f$. This operator preserves the smoothness classes determined by regular majorants, and is seen to be compact on these classes precisely when none of the measures $\tau_\alpha$ has an atomic part. In the process, a duality theorem for smoothness classes is proved, improving a result of Shields and Williams, and various theorems about composition operators on weighted Bergman spaces are extended to spaces arising from regular weights.

Cited by 0Open access

Operators

ACM SIGAPL APL Quote Quad · 1983

The forms in this section are referred to as operators. Operators take scalar functions as arguments and produce functions, called derived functions, as results. For example, the operator reduction takes a single dyadic scalar-function as an argument and produces a monadic function as a result.Because f is restricted to scalar functions, the derived functions produced by scan and reduction may be viewed either as being applied between subarrays of rank 0⌈ - 1+ρρ B or as being repeated on vector subarrays. As an expository device, the evaluation sequences in this document use the vector definition.

Cited by 0

Operators

2012

Operators are symbols used in statements and expressions to request specific actions. They operate on operands or arguments (e.g., variables and constants). This chapter looks at operators in four categories: the (a) assignment operator; (b) arithmetic/mathematical operators; (c) relational operators and (4) logical operators. C++ includes a modulus operator represented by the symbol %, which is used to produce the remainder of an integer division. C++ includes unary operators: an increment operator represented by ++ and a decrement operator represented by –. They need only one operand and they decrease or increase the value of the operand (whether integer or floating point) by 1. The relational operators are limited to testing the relationship between the values of two expressions at a time and that too for a few simple relationships. C++ provides three logical operators “AND, OR and NOT” that one can combine with the relational operators to carry out tests that are a little more complex to a lot more.

Cited by 0

Operators

Mikael Olsson · Apress eBooks · 2020

A numeric operator is a symbol that makes the script perform a specific mathematical or logical manipulation. The numeric operators can be grouped into five types: arithmetic, assignment, comparison, logical, and bitwise operators.

Cited by 0

Operators

Jay Bryant · Apress eBooks · 2012

Java includes many operators, from ordinary mathematical operators such as a minus sign (−) to operators that only make sense for object-oriented programming, such as instanceof.

Cited by 0

Operators

Slobodan Dmitrović · Apress eBooks · 2021

Operators are an essential part of the language. This section explains what they are and how they are used. It might seem that there is plenty of theory surrounding this subject, but do not worry. We need to adopt the theoretical part to use it in practical code examples later in the book.

Cited by 1