scholarly journals Numerical ranges of uniformly continuous functions on the unit sphere of a Banach space

2004 ◽  
Vol 297 (2) ◽  
pp. 472-476 ◽  
Author(s):  
Ángel Rodrı́guez Palacios
Keyword(s):  
Banach Space ◽  
Unit Sphere ◽  
Continuous Functions ◽  
Uniformly Continuous

Homomorphisms Between Algebras of Continuous Functions

1989 ◽  
Vol 41 (1) ◽  
pp. 132-162 ◽  
Author(s):  
J. G. Llavona ◽  
J. A. Jaramillo
Keyword(s):  
Banach Space ◽  
Continuous Functions ◽  
Point Of View ◽  
Space Theory ◽  
Infinite Dimensional ◽  
Weakly Continuous ◽  
Dimensional Approximation ◽  
Weak Topologies ◽  
Bounded Sets ◽  
Uniformly Continuous

We are concerned in this paper with the study of homomorphisms between different algebras of continuous functions, especially the algebras of real functions which are either weakly continuous on bounded sets or weakly uniformly continuous on bounded sets on a Banach space (see definitions below).These spaces of weakly [uniformly] continuous functions appeared in relation with some questions in Infinite-dimensional Approximation Theory (see [4], [6], [11], [12], [13] and [16]); and since the structure of these function spaces is closely related with properties of different weak topologies (the bounded-weak and bounded-weak* topologies, respectively) and with the structure of Banach spaces on which they are defined, their study also presents interest from the point of view of Banach space theory, as can be seen in [2], [12] or [17].

WEAKLY COMPACT HOMOMORPHISMS BETWEEN SMALL ALGEBRAS OF ANALYTIC FUNCTIONS

2001 ◽  
Vol 33 (6) ◽  
pp. 715-726 ◽  
Author(s):  
PABLO GALINDO ◽  
MIKAEL LINDSTRÖM
Keyword(s):  
Banach Space ◽  
Composition Operator ◽  
Analytic Functions ◽  
Approximation Property ◽  
Composition Operators ◽  
Continuous Functions ◽  
Weak Compactness ◽  
Weakly Compact ◽  
The Relationship ◽  
Uniformly Continuous

The weak compactness of the composition operator CΦ(f) = f ○ Φ acting on the uniform algebra of analytic uniformly continuous functions on the unit ball of a Banach space with the approximation property is characterized in terms of Φ. The relationship between weak compactness and compactness of these composition operators and general homomorphisms is also discussed.

Gradient-like parabolic semiflows on BUC(ℝN)

1998 ◽  
Vol 128 (6) ◽  
pp. 1281-1291 ◽  
Author(s):  
Daniel Daners ◽  
Sandro Merino
Keyword(s):  
Banach Space ◽  
Exponential Decay ◽  
Decay Estimate ◽  
Reaction Diffusion ◽  
Continuous Functions ◽  
Stationary Solutions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Uniformly Continuous

We prove that a class of weighted semilinear reaction diffusion equations on RN generates gradient-like semiflows on the Banach space of bounded uniformly continuous functions on RN. If N = 1 we show convergence to a single equilibrium. The key for getting the result is to show the exponential decay of the stationary solutions, which is obtained by means of a decay estimate of the kernel of the underlying semigroup.

scholarly journals Preimages of Residual Sets of Continuous Functions under Operation of Superposition

2005 ◽  
Vol 12 (4) ◽  
pp. 763-768
Author(s):  
Artur Wachowicz
Keyword(s):  
Banach Space ◽  
Continuous Functions ◽  
Real Functions ◽  
Second Category ◽  
Residual Sets

Abstract Let 𝐶 = 𝐶[0, 1] denote the Banach space of continuous real functions on [0, 1] with the sup norm and let 𝐶* denote the topological subspace of 𝐶 consisting of functions with values in [0, 1]. We investigate the preimages of residual sets in 𝐶 under the operation of superposition Φ : 𝐶 × 𝐶* → 𝐶, Φ(𝑓, 𝑔) = 𝑓 ○ 𝑔. Their behaviour can be different. We show examples when the preimages of residual sets are nonresidual of second category, or even nowhere dense, and examples when the preimages of nontrivial residual sets are residual.

scholarly journals Towards the fixed point property for superreflexive spaces

2001 ◽  
Vol 64 (3) ◽  
pp. 435-444 ◽  
Author(s):  
Andrzej Wiśnicki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unit Sphere ◽  
Convex Set ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Geometrical Condition

A Banach space X is said to have property (Sm) if every metrically convex set A ⊂ X which lies on the unit sphere and has diameter not greater than one can be (weakly) separated from zero by a functional. We show that this geometrical condition is closely connected with the fixed point property for nonexpansive mappings in superreflexive spaces.

scholarly journals Lattices of uniformly continuous functions

2013 ◽  
Vol 160 (1) ◽  
pp. 50-55 ◽  
Author(s):  
Félix Cabello Sánchez ◽  
Javier Cabello Sánchez
Keyword(s):  
Continuous Functions ◽  
Uniformly Continuous

scholarly journals BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY

2007 ◽  
Vol 49 (1) ◽  
pp. 145-154
Author(s):  
BRUCE A. BARNES
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Integral Operators ◽  
Continuous Functions ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Closed Range ◽  
Bounded Linear ◽  
Spaces Of Continuous Functions

Abstract.LetTbe a bounded linear operator on a Banach spaceW, assumeWandYare in normed duality, and assume thatThas adjointT†relative toY. In this paper, conditions are given that imply that for all λ≠0, λ−Tand λ −T†maintain important standard operator relationships. For example, under the conditions given, λ −Thas closed range if, and only if, λ −T†has closed range.These general results are shown to apply to certain classes of integral operators acting on spaces of continuous functions.

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.

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