scholarly journals On the M-hypercyclicity of cosine function on Banach spaces

2019 ◽  
Vol 38 (3) ◽  
pp. 133-140
Author(s):  
Abdelaziz Tajmouati ◽  
Abdeslam El Bakkali ◽  
Ahmed Toukmati
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Complex Banach Space ◽  
Cosine Function ◽  
Infinite Dimensional ◽  
Uniformly Continuous

In this paper we introduce and study the M-hypercyclicity of strongly continuous cosine function on separable complex Banach space, and we give the criteria for cosine function to be M-hypercyclic. We also prove that every separable infinite dimensional complex Banach space admits a uniformly continuous cosine function.

scholarly journals Isometries on extremely non-complex Banach spaces

2010 ◽  
Vol 10 (2) ◽  
pp. 325-348 ◽  
Author(s):  
Piotr Koszmider ◽  
Miguel Martín ◽  
Javier Merí
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Real Banach Space ◽  
Complex Banach Space ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Group Of Isometries

AbstractGiven a separable Banach space E, we construct an extremely non-complex Banach space (i.e. a space satisfying that ‖ Id + T2 ‖ = 1 + ‖ T2 ‖ for every bounded linear operator T on it) whose dual contains E* as an L-summand. We also study surjective isometries on extremely non-complex Banach spaces and construct an example of a real Banach space whose group of surjective isometries reduces to ±Id, but the group of surjective isometries of its dual contains the group of isometries of a separable infinite-dimensional Hilbert space as a subgroup.

scholarly journals Entire Analytic Functions of Unbounded Type on Banach Spaces and Their Lineability

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 150
Author(s):  
Andriy Zagorodnyuk ◽  
Anna Hihliuk
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Entire Functions ◽  
Dimensional Algebra ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Linear Subspaces ◽  
Infinite Dimensional Banach Space

In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the set of entire functions of unbounded type can be represented as a union of infinite dimensional linear subspaces (without the origin). Moreover, we show that for some cases, the set of entire functions of unbounded type generated by a given sequence of polynomials contains an infinite dimensional algebra (without the origin). Some applications for symmetric analytic functions on Banach spaces are obtained.

scholarly journals Characteristic Functions and Borel Exceptional Values ofE-Valued Meromorphic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zhaojun Wu ◽  
Zuxing Xuan
Keyword(s):  
Banach Space ◽  
Meromorphic Functions ◽  
Complex Banach Space ◽  
Schauder Basis ◽  
Characteristic Functions ◽  
Infinite Dimensional ◽  
Borel Exceptional Values

The main purpose of this paper is to investigate the characteristic functions and Borel exceptional values ofE-valued meromorphic functions from theℂR={z:|z|<R},  0<R≤+∞to an infinite-dimensional complex Banach spaceEwith a Schauder basis. Results obtained extend the relative results by Xuan, Wu and Yang, Bhoosnurmath, and Pujari.

Holomorphic functions with distinguished properties on infinite dimensional spaces

2018 ◽  
Vol 70 (3) ◽  
pp. 797-811
Author(s):  
Thiago R Alves ◽  
Geraldo Botelho
Keyword(s):  
Banach Space ◽  
Holomorphic Functions ◽  
Complex Banach Space ◽  
Algebraic Structures ◽  
Infinite Dimensional ◽  
Zero Function ◽  
Bounded Holomorphic

Abstract In this paper, we develop a method to construct holomorphic functions that exist only on infinite dimensional spaces. The following types of holomorphic functions f:U→ℂ on some open subsets U of an infinite dimensional complex Banach space are constructed: (1) f is bounded holomorphic on U and is continuously, but not uniformly continuously extended to U¯; (2) f is continuous on U¯ and holomorphic of bounded type on U, but f is unbounded on U; (3) f is holomorphic of bounded type on U and f cannot be continuously extended to U¯. The technique we develop is powerful enough to provide, in the cases (2) and (3) above, large algebraic structures formed by such functions (up to the zero function, of course).

scholarly journals Multipliers on Vector Valued Bergman Spaces

2002 ◽  
Vol 54 (6) ◽  
pp. 1165-1186 ◽  
Author(s):  
Oscar Blasco ◽  
José Luis Arregui
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Bergman Space ◽  
Unit Disc ◽  
Bergman Spaces ◽  
Complex Banach Space ◽  
Bounded Operators ◽  
Taylor Coefficients ◽  
Vector Valued

AbstractLet X be a complex Banach space and let Bp(X) denote the vector-valued Bergman space on the unit disc for 1 ≤ p < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y defines a multiplier between Bp(X) and Bq(Y) (resp. Bp(X) and lq(Y)) if for any function we have that belongs to Bq(Y) (resp. (Tn(xn))n ∈ lq(Y)). Several results on these multipliers are obtained, some of them depending upon the Fourier or Rademacher type of the spaces X and Y. New properties defined by the vector-valued version of certain inequalities for Taylor coefficients of functions in Bp(X) are introduced.

scholarly journals Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 133
Author(s):  
Andriy Zagorodnyuk ◽  
Anna Hihliuk
Keyword(s):  
Banach Space ◽  
Analytic Function ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Main Question ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Infinite Dimensional Banach Space ◽  
Taylor Polynomials

In this paper we investigate analytic functions of unbounded type on a complex infinite dimensional Banach space X. The main question is: under which conditions is there an analytic function of unbounded type on X such that its Taylor polynomials are in prescribed subspaces of polynomials? We obtain some sufficient conditions for a function f to be of unbounded type and show that there are various subalgebras of polynomials that support analytic functions of unbounded type. In particular, some examples of symmetric analytic functions of unbounded type are constructed.

scholarly journals On a local degree for a class of multi-valued vector fields in infinite dimensional Banach spaces

1996 ◽  
Vol 1 (4) ◽  
pp. 381-396 ◽  
Author(s):  
N. M. Benkafadar ◽  
B. D. Gel'man
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Vector Fields ◽  
Existence Of Solutions ◽  
Index Zero ◽  
Compact Mapping ◽  
Infinite Dimensional ◽  
Upper Semicontinuous ◽  
Local Degree

This paper is devoted to the development of a local degree for multi-valued vector fields of the formf−F. Here,fis a single-valued, proper, nonlinear, Fredholm,C1-mapping of index zero andFis a multi-valued upper semicontinuous, admissible, compact mapping with compact images. The mappingsfandFare acting from a subset of a Banach spaceEinto another Banach spaceE1. This local degree is used to investigate the existence of solutions of a certain class of operator inclusions.

scholarly journals Milloux Inequality ofE-Valued Meromorphic Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Zhaojun Wu ◽  
Zuxing Xuan
Keyword(s):  
Banach Space ◽  
Meromorphic Function ◽  
Complex Plane ◽  
Complex Banach Space ◽  
Schauder Basis ◽  
Infinite Dimensional ◽  
Borel Exceptional Values

The main purpose of this paper is to establish the Milloux inequality ofE-valued meromorphic function from the complex planeℂto an infinite dimensional complex Banach spaceEwith a Schauder basis. As an application, we study the Borel exceptional values of anE-valued meromorphic function and those of its derivatives; results are obtained to extend some related results for meromorphic scalar-valued function of Singh, Gopalakrishna, and Bhoosnurmath.

scholarly journals ON A CHARACTERISTIC PROPERTY OF FINITE-DIMENSIONAL BANACH SPACES

2011 ◽  
Vol 53 (3) ◽  
pp. 443-449 ◽  
Author(s):  
ANTONÍN SLAVÍK
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Characteristic Property ◽  
Linear Operators ◽  
Infinite Dimensional ◽  
Counter Example ◽  
Finite Dimensional ◽  
Infinite Dimensional Banach Space ◽  
Dvoretzky’S Theorem ◽  
The Given

AbstractThis paper is inspired by a counter example of J. Kurzweil published in [5], whose intention was to demonstrate that a certain property of linear operators on finite-dimensional spaces need not be preserved in infinite dimension. We obtain a stronger result, which says that no infinite-dimensional Banach space can have the given property. Along the way, we will also derive an interesting proposition related to Dvoretzky's theorem.

scholarly journals Nonwandering operators in Banach space

2005 ◽  
Vol 2005 (24) ◽  
pp. 3895-3908 ◽  
Author(s):  
Lixin Tian ◽  
Jiangbo Zhou ◽  
Xun Liu ◽  
Guangsheng Zhong
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sequence Space ◽  
Separable Banach Space ◽  
Infinite Dimensional ◽  
Banach Sequence Space ◽  
Background Space ◽  
Physical Background ◽  
Structurally Stable ◽  
Banach Sequence

We introduce nonwandering operators in infinite-dimensional separable Banach space. They are new linear chaotic operators and are relative to hypercylic operators, but different from them. Firstly, we show some examples for nonwandering operators in some typical infinite-dimensional Banach spaces, including Banach sequence space and physical background space. Then we present some properties of nonwandering operators and the spectra decomposition of invertible nonwandering operators. Finally, we obtain that invertible nonwandering operators are locally structurally stable.

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