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

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

scholarly journals UNCONDITIONAL CONVERGENCE IN THE STRONG OPERATOR TOPOLOGY AND ℓ∞

2011 ◽  
Vol 53 (3) ◽  
pp. 583-598 ◽  
Author(s):  
IOANA GHENCIU ◽  
PAUL LEWIS
Keyword(s):  
Banach Space ◽  
Vector Measure ◽  
Strong Operator Topology ◽  
Unconditional Convergence ◽  
Fundamental Result ◽  
Boundedness Theorem ◽  
Strong Operator ◽  
Spaces Of Operators ◽  
Funct Anal ◽  
Nikodym Theorem

AbstractIn this paper we study non-complemented spaces of operators and the embeddability of ℓ∞ in the spaces of operators L(X, Y), K(X, Y) and Kw*(X*, Y). Results of Bator and Lewis [2, 3] (Bull. Pol. Acad. Sci. Math.50(4) (2002), 413–416; Bull. Pol. Acad. Sci. Math.549(1) (2006), 63–73), Emmanuele [8–10] (J. Funct. Anal.99 (1991), 125–130; Math. Proc. Camb. Phil. Soc.111 (1992), 331–335; Atti. Sem. Mat. Fis. Univ. Modena42(1) (1994), 123–133), Feder [11] (Canad. Math. Bull.25 (1982), 78–81) and Kalton [16] (Math. Ann.208 (1974), 267–278), are generalised. A vector measure result is used to study the complementation of the spaces W(X, Y) and K(X, Y) in the space L(X, Y), as well as the complementation of K(X, Y) in W(X, Y). A fundamental result of Drewnowski [7] (Math. Proc. Camb. Phil. Soc. 108 (1990), 523–526) is used to establish a result for operator-valued measures, from which we obtain as corollaries the Vitali–Hahn–Saks–Nikodym theorem, the Nikodym Boundedness theorem and a Banach space version of the Phillips Lemma.

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

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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