scholarly journals The Multivariate Müntz-Szasz Problem in Weighted Banach Space onRn

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xiangdong Yang
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Uniform Norm ◽  
Continuous Functions ◽  
Real Numbers ◽  
Weighted Banach Space ◽  
Weighted Banach Spaces

The purpose of this paper is to give an extension of Müntz-Szasz theorems to multivariable weighted Banach space. Denote by{λk=(λk1,λk2,...,λkn)}k=1∞a sequence of real numbers inR+n. The completeness of monomials{tλk}inCαis investigated, whereCαis the weighted Banach spaces which consist of complex continuous functionsfdefined onRnwithf(t)exp(-α(t))vanishing at infinity in the uniform norm.

Minimality and Closeure of Random Exponential Systems

2011 ◽  
Vol 130-134 ◽  
pp. 188-190
Author(s):  
Feng Yan ◽  
Xiao Ling Liu ◽  
Su Mei Zhang
Keyword(s):  
Banach Space ◽  
Entire Function ◽  
Dirichlet Series ◽  
Uniform Norm ◽  
Continuous Functions ◽  
Weighted Banach Space

In this paper, we study the minimality properties of random exponential systems in , where is a weighted Banach space of complex continuous functions of on with vanishing at infinity, in the uniform norm with respect to the weight . We prove that, if is incomplete in , then is minimal and each function in can be extended to an entire function respresented by a Dirichlet series.

scholarly journals EXPONENTIAL POLYNOMIAL APPROXIMATION OF WEIGHTED BANACH SPACE ON ℝn

2012 ◽  
Vol 55 (1) ◽  
pp. 115-121 ◽  
Author(s):  
XIANGDONG YANG
Keyword(s):  
Banach Space ◽  
Polynomial Approximation ◽  
Sufficient Conditions ◽  
Uniform Norm ◽  
Continuous Functions ◽  
Necessary And Sufficient Conditions ◽  
Exponential Polynomial ◽  
Exponential System ◽  
Weighted Banach Space ◽  
Necessary And Sufficient

AbstractNecessary and sufficient conditions for the incompleteness of exponential system in Cα are characterised, where Cα is the weighted Banach space of complex continuous functions f defined on ℝn with f(t)exp(−α(t)) vanishing at infinity in the uniform norm.

Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

1999 ◽  
Vol 42 (2) ◽  
pp. 139-148 ◽  
Author(s):  
José Bonet ◽  
Paweł Dománski ◽  
Mikael Lindström
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Point Evaluation ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

AbstractEvery weakly compact composition operator between weighted Banach spaces of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

scholarly journals The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space

2013 ◽  
Vol 21 (3) ◽  
pp. 185-191
Author(s):  
Keiko Narita ◽  
Noboru Endou ◽  
Yasunari Shidama
Keyword(s):  
Banach Space ◽  
Integral Operator ◽  
Real Banach Space ◽  
Closed Interval ◽  
Continuous Functions ◽  
Real Numbers ◽  
Riemann Integral ◽  
Basic Properties ◽  
Bounded Functions ◽  
Definition Of

Summary In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems introduced in the article [9] and the article [11] to the proof. Using the definition of the article [10], we also proved some theorems on bounded functions.

scholarly journals On some dichotomy concepts with different growth rates for evolution operators in Banach spaces

2015 ◽  
Vol 53 (2) ◽  
pp. 133-150
Author(s):  
Nicolae Marian Seimeanu
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Growth Rates ◽  
Real Numbers ◽  
Evolution Operators

Abstract This paper treats three concepts of (h, k)-dichotomy and their correspondents in the uniform cases. The connections between them are established through examples and counterexamples presented on the Banach space of square-summable sequences of real numbers.

scholarly journals On Weighted Polynomial Approximation With Gaps

2005 ◽  
Vol 178 ◽  
pp. 55-61 ◽  
Author(s):  
Guantie Deng
Keyword(s):  
Banach Space ◽  
Continuous Function ◽  
Polynomial Approximation ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Weighted Polynomial Approximation ◽  
Necessary And Sufficient Condition ◽  
Weighted Banach Space ◽  
Nonnegative Continuous Function ◽  
Necessary And Sufficient

Let α be a nonnegative continuous function on ℝ. In this paper, the author obtains a necessary and sufficient condition for polynomials with gaps to be dense in Cα, where Cα is the weighted Banach space of complex continuous functions ƒ on ℝ with ƒ(t) exp(−α(t)) vanishing at infinity.

scholarly journals Convergence of weighted sums of independent random variables and an extension to Banach space-valued random variables

1979 ◽  
Vol 2 (2) ◽  
pp. 309-323
Author(s):  
W. J. Padgett ◽  
R. L. Taylor
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Real Numbers ◽  
Martingale Theory ◽  
Random Elements ◽  
Schauder Bases

Let{Xk}be independent random variables withEXk=0for allkand let{ank:n≥1, k≥1}be an array of real numbers. In this paper the almost sure convergence ofSn=∑k=1nankXk,n=1,2,…, to a constant is studied under various conditions on the weights{ank}and on the random variables{Xk}using martingale theory. In addition, the results are extended to weighted sums of random elements in Banach spaces which have Schauder bases. This extension provides a convergence theorem that applies to stochastic processes which may be considered as random elements in function spaces.

scholarly journals Factoring absolutely summing operators through Hilbert-Schmidt operators

1989 ◽  
Vol 31 (2) ◽  
pp. 131-135 ◽  
Author(s):  
Hans Jarchow
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hausdorff Space ◽  
Bounded Operator ◽  
Continuous Functions ◽  
Space Of Continuous Functions ◽  
Reflexive Banach Spaces ◽  
Summing Operator ◽  
Schmidt Operator ◽  
Second Dual

Let K be a compact Hausdorff space, and let C(K) be the corresponding Banach space of continuous functions on K. It is well-known that every 1-summing operator S:C(K)→l2 is also nuclear, and therefore factors S = S1S2, with S1:l2→l2 a Hilbert–Schmidt operator and S1:C(K)→l2 a bounded operator. It is easily seen that this latter property is preserved when C(K) is replaced by any quotient, and that a Banach space X enjoys this property if and only if its second dual, X**, does. This led A. Pełczyński [15] to ask if the second dual of a Banach space X must be isomorphic to a quotient of a C(K)-space if X has the property that every 1-summing operator X-→l2 factors through a Hilbert-Schmidt operator. In this paper, we shall first of all reformulate the question in an appropriate manner and then show that counter-examples are available among super-reflexive Tsirelson-like spaces as well as among quasi-reflexive Banach spaces.

scholarly journals A Remark on the Continuity of the Dual Process

1968 ◽  
Vol 32 ◽  
pp. 287-295 ◽  
Author(s):  
Mamoru Kanda
Keyword(s):  
Banach Space ◽  
Compact Support ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Finite Measure ◽  
Uniform Norm ◽  
Continuous Functions ◽  
Dual Process ◽  
Space Of Continuous Functions ◽  
Locally Compact

Let S be a locally compact (not compact) Hausdorff space satisfying the second axiom of countability and let ℬ be the σ field of all Borel subsets of S and let A be the σ-field of all the subsets of S which, for each finite measure μ defined on (S, A), are in the completed σ field of ℬ relative to μ. We denote by C0 the Banach space of continuous functions vanishing at infinity with the uniform norm and Bk the space of bounded A-measurable functions with compact support in S.

scholarly journals Averaging distances in certain Banach spaces

1997 ◽  
Vol 55 (1) ◽  
pp. 147-160 ◽  
Author(s):  
Reinhard Wolf
Keyword(s):  
Banach Space ◽  
Hausdorff Space ◽  
Finite Dimension ◽  
Closed Interval ◽  
Continuous Functions ◽  
Real Numbers ◽  
Empty Interval ◽  
Positive Real ◽  
Complete Discussion ◽  
Image Position

Let E be a Banach space. The averaging interval AI(E) is defined as the set of positive real numbers α, with the following property: For each n ∈ ℕ and for all (not necessarily distinct) x1, x2, … xn ∈ E with ∥x1∥ = ∥x2∥ = … = ∥xn∥ = 1, there is an x ∈ E, ∥x∥ = 1, such thatIt follows immediately, that AI(E) is a (perhaps empty) interval included in the closed interval [1,2]. For example in this paper it is shown that AI(E) = {α} for some 1 < α < 2, if E has finite dimension. Furthermore a complete discussion of AI(C(X)) is given, where C(X) denotes the Banach space of real valued continuous functions on a compact Hausdorff space X. Also a Banach space E is found, such that AI(E) = [1,2].

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