Banach Spaces of Vector-Valued Functions

1997 ◽  
Author(s):  
Pilar Cembranos ◽  
José Mendoza
Keyword(s):  
Banach Spaces ◽  
Vector Valued Functions ◽  
Vector Valued

Multipliers for vector valued functions

1984 ◽  
Vol 99 (1-2) ◽  
pp. 137-143
Author(s):  
José Luis Torrea
Keyword(s):  
Abelian Group ◽  
Banach Spaces ◽  
Compact Abelian Group ◽  
Locally Compact Abelian Group ◽  
Lebesgue Spaces ◽  
Locally Compact ◽  
Translation Invariant ◽  
Bounded Linear ◽  
Vector Valued Functions ◽  
Vector Valued

SynopsisLet G be a locally compact abelian group and let Γ be the dual of G. Let A, B be Banach spaces and Lp(G,A) the Bochner-Lebesgue spaces. We prove that the space of bounded linear translation invariant operators from L1(G, A) to LX(G, B) can be identified with the space of bounded convolution invariant (in some sense) operators and also with the space of a(A, B)-valued “weak regular” measures with the relation Tf = f *μ. (A. The existence of a function m∈ L∞ (Γ,α(A,B)), such that is also proved.

scholarly journals Local dual spaces of Banach spaces of vector-valued functions

2002 ◽  
Vol 130 (11) ◽  
pp. 3255-3258 ◽  
Author(s):  
Manuel González ◽  
Antonio Martínez-Abejón
Keyword(s):  
Banach Spaces ◽  
Dual Spaces ◽  
Vector Valued Functions ◽  
Vector Valued

Square Banach spaces

1969 ◽  
Vol 66 (3) ◽  
pp. 553-558 ◽  
Author(s):  
F. Cunningham
Keyword(s):  
Banach Spaces ◽  
Real Banach Space ◽  
Uniform Norm ◽  
Banach Lattices ◽  
One Dimensional ◽  
Upper Semicontinuous ◽  
Negative Function ◽  
Isometric Representation ◽  
Vector Valued Functions ◽  
Vector Valued

In (2) I described a canonical isometric representation of an arbitrary real Banach space X by vector-valued functions (with the uniform norm) on a compact Hausdorif space ω with the following properties: (1) the representing function space is invariant under multiplications by continuous real functions on ω; (2) the norm of each representing function, as a real non-negative function on ω, is upper semicontinuous; and (3) this decomposition of X is maximally fine. I called attention to the class of spaces X for which at every point of ω the component space of this representation is one-dimensional or 0, so that the representing functions are in effect real valued. I propose to call such Banach spaces square, because of the shape of the unit ball in the two-dimensional case. In (2) I stated without proof, erroneously as it turns out, that the class of square spaces coincides with what Lindenstrauss in (4) called G-spaces. The primary purpose of this paper is to show that the class of square spaces is actually properly contained in that of G-spaces. It is known ((2), p. 620, Example 1) that it contains properly the class of continuous function spaces C(ω). Among G-spaces are the M-spaces treated by Kakutani as Banach lattices (3). I shall show further that neither class, square spaces or M-spaces (regarded now purely as Banach spaces), contains the other.

scholarly journals Weighted Vector-Valued Holomorphic Functions on Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Enrique Jordá
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Holomorphic Functions ◽  
Connected Subset ◽  
Weighted Banach Spaces ◽  
Vector Valued Functions ◽  
Vector Valued

We study the weighted Banach spaces of vector-valued holomorphic functions defined on an open and connected subset of a Banach space. We use linearization results on these spaces to get conditions which ensure that a functionfdefined in a subsetAof an open and connected subsetUof a Banach spaceX, with values in another Banach spaceE, and admitting certain weak extensions in a Banach space of holomorphic functions can be holomorphically extended in the corresponding Banach space of vector-valued functions.

scholarly journals On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces

2012 ◽  
Vol 355 (4) ◽  
pp. 1201-1219 ◽  
Author(s):  
M. Jiménez-Sevilla ◽  
L. Sánchez-González
Keyword(s):  
Banach Spaces ◽  
Vector Valued Functions ◽  
Vector Valued

scholarly journals BANACH SPACES OF CONTINUOUS VECTOR-VALUED FUNCTIONS OF ORDINALS

2001 ◽  
Vol 44 (1) ◽  
pp. 49-62 ◽  
Author(s):  
Elói Medina Galego
Keyword(s):  
Banach Spaces ◽  
Continuum Hypothesis ◽  
Ordinal Number ◽  
Supremum Norm ◽  
Vector Valued Functions ◽  
Isomorphic Classification ◽  
Vector Valued ◽  
The Continuum

AbstractLet $X$ be a Banach space and $\xi$ an ordinal number. We study some isomorphic classifications of the Banach spaces $X^\xi$ of the continuous $X$-valued functions defined in the interval of ordinals $[1,\xi]$ and equipped with the supremum norm. More precisely, first we use the continuum hypothesis to give an isomorphic classification of $C(I)^\xi$, $\xi\geq\omega_1$. Then we present a characterization of the separable Banach spaces $X$ that are isomorphic to $X^\xi$, $\forall\xi$, $\omega\leq\xi lt \omega_1$. Finally, we show that the isomorphic classifications of $(C(I)\oplus F^*)^\xi$ and $\ell_\infty(\N)^\xi$, where $F$ is the space of Figiel and $\omega\leq\xi lt \omega_1$ are similar to that of $\R^\xi$ given by Bessaga and Pelczynski.AMS 2000 Mathematics subject classification: Primary 46B03; 46B20; 46E15

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