scholarly journals Spaces of integrable functions with respect to a vector measure and factorizations through Lp and Hilbert spaces

2007 ◽  
Vol 330 (2) ◽  
pp. 1249-1263 ◽  
Author(s):  
A. Fernández ◽  
F. Mayoral ◽  
F. Naranjo ◽  
C. Sáez ◽  
E.A. Sánchez-Pérez
Keyword(s):  
Hilbert Spaces ◽  
Vector Measure ◽  
Integrable Functions

Strong factorization of operators on spaces of vector measure integrable functions and unconditional convergence of series

2007 ◽  
Vol 257 (2) ◽  
pp. 381-402 ◽  
Author(s):  
J. M. Calabuig ◽  
F. Galaz-Fontes ◽  
E. Jiménez-Fernández ◽  
E. A. Sánchez Pérez
Keyword(s):  
Vector Measure ◽  
Unconditional Convergence ◽  
Convergence Of Series ◽  
Integrable Functions

VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES OF INTEGRABLE FUNCTIONS AND MERCER THEOREM

2006 ◽  
Vol 04 (04) ◽  
pp. 377-408 ◽  
Author(s):  
CLAUDIO CARMELI ◽  
ERNESTO DE VITO ◽  
ALESSANDRO TOIGO
Keyword(s):  
Integral Operator ◽  
Hilbert Spaces ◽  
Spectral Decomposition ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Spaces ◽  
Integrable Functions ◽  
Kernel Hilbert Spaces ◽  
Vector Valued

We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2, we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending the Mercer theorem.

scholarly journals Multiplication operators on spaces of integrable functions with respect to a vector measure

2008 ◽  
Vol 343 (1) ◽  
pp. 514-524 ◽  
Author(s):  
R. del Campo ◽  
A. Fernández ◽  
I. Ferrando ◽  
F. Mayoral ◽  
F. Naranjo
Keyword(s):  
Vector Measure ◽  
Multiplication Operators ◽  
Integrable Functions

Commutative Sequences of Integrable Functions and Best Approximation With Respect to the Weighted Vector Measure Distance

2005 ◽  
Vol 54 (4) ◽  
pp. 495-510 ◽  
Author(s):  
L. M. García. Raffi ◽  
E. A. Sánchez. Pérez ◽  
J. V. Sánchez. Pérez
Keyword(s):  
Best Approximation ◽  
Vector Measure ◽  
Integrable Functions

scholarly journals Convolution-continuous bilinear operators acting on Hilbert spaces of integrable functions

2018 ◽  
Vol 9 (2) ◽  
pp. 166-179 ◽  
Author(s):  
Ezgi Erdoğan ◽  
José M. Calabuig ◽  
Enrique A. Sánchez Pérez
Keyword(s):  
Hilbert Spaces ◽  
Bilinear Operators ◽  
Integrable Functions

scholarly journals Biconcave-function characterisations of UMD and Hilbert spaces

1993 ◽  
Vol 47 (2) ◽  
pp. 297-306 ◽  
Author(s):  
Jinsik Mok Lee
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Hilbert Spaces ◽  
Complex Banach Space ◽  
Unit Interval ◽  
Martingale Differences ◽  
Almost Everywhere ◽  
Integrable Functions ◽  
Image Position ◽  
Umd Banach Spaces

Suppose that X is a real or complex Banach space with norm |·|. Then X is a Hilbert space if and only iffor all x in X and all X-valued Bochner integrable functions Y on the Lebesgue unit interval satisfying EY = 0 and |x − Y| ≤ 2 almost everywhere. This leads to the following biconcave-function characterisation: A Banach space X is a Hilbert space if and only if there is a biconcave function η: {(x, y) ∈ X × X: |x − y| ≤ 2} → R such that η(0, 0) = 2 andIf the condition η(0, 0) = 2 is eliminated, then the existence of such a function η characterises the class UMD (Banach spaces with the unconditionally property for martingale differences).

Lattice copies of c0and l∞in spaces of integrable functions for a vector measure

2014 ◽  
Vol 500 ◽  
pp. 1-68 ◽  
Author(s):  
S. Okada ◽  
W. J. Ricker ◽  
E. A. Sánchez Pérez
Keyword(s):  
Vector Measure ◽  
Integrable Functions
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