✦ LIBER ✦

Factorization of Completely Bounded Bilinear Operators and Injectivity

✍ Scribed by Allan M Sinclair; Roger R Smith

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 345 KB
Volume: 157
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3260

No coin nor oath required. For personal study only.

✦ Synopsis

A completely bounded bilinear operator ,: M_M Ä M on a von Neumann algebra M is said to have a factorization in M if there exist completely bounded linear operators j , % j : M Ä M such that ,(x, y)= :

where convergence of the sum is made precise below. The main result of the paper is that all completely bounded bilinear operators ,: M_M Ä M have factorizations in M if and only if M is injective.

📜 SIMILAR VOLUMES

A Factorization Property of R-Bounded Se

A Factorization Property of R-Bounded Sets of Operators on Lp-Spaces

✍ Christian Le Merdy; Arnaud Simard 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 188 KB 👁 2 views

On summability of bilinear operators

✍ Daniel Carando; Verónica Dimant 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 155 KB

## Abstract We study some properties of strongly and absolutely __p__‐summing bilinear operators. We show that Hilbert‐Schmidt bilinear mappings are both strongly and absolutely __p__‐summing, for every __p__ ≥ 1. Giving an example of a strongly 1‐summing bilinear mapping which fails to be weakly c

Factorization of Tent Spaces and Hankel

Factorization of Tent Spaces and Hankel Operators

✍ W.S. Cohn; I.E. Verbitsky 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 187 KB

It is shown that the factorization T p q =T p } T q for tent spaces proved by R. R. Coifman et al. (1985, J. Funct. Anal. 62, 304 335) for p>q, q=2, holds true for all 0<p, q< . From this certain strong factorization theorems are derived for spaces H p s of fractional derivatives of H p functions, a

Banach Lattices of Bounded Operators

✍ H.-U. Schwarz 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 334 KB

Banach Lattices of Bounded Operators By H.-U. SCHWARZ (Jena) (Eingegangen am 1.3.1977) There are given two equivalent methods to construct BANACE lattices of compact operators. All known examples of such lattices are included.

Duality of Type H1-BMO and Bilinear Oper

Duality of Type H1-BMO and Bilinear Operators

✍ A. Youssfi 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 299 KB

Bounded Operators and Complemented Subsp

Bounded Operators and Complemented Subspaces of Cartesian Products

✍ P. Djakov; T. Terzioğlu; M. Yurdakul; V. Zahariuta 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 157 KB

## Abstract We study the structure of complemented subspaces in Cartesian products __X__ × __Y__ of Köthe spaces __X__ and __Y__ under the assumption that every linear continuous operator from __X__ to __Y__ is bounded. In particular, it is proved that each non‐Montel complemented subspace with abs