✦ LIBER ✦

On Banach Spaces with Bases

✍ Scribed by Wolfgang Lusky

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 568 KB
Volume: 138
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1996.0070

No coin nor oath required. For personal study only.

✦ Synopsis

We show that a Banach space X has a basis provided there are bounded linear finite rank operators R n : X Ä X such that lim n R n x=x for all x # X, R m R n =R min(m, n) if m{n, and R n &R n&1 factors uniformly through l mn p 's for some p. As an application we obtain conditions on a subset 4/Z such that C 4 =closed span[z k : k # 4]/ C(T) and L 4 =closed span[z k : k # 4]/L 1 (T) have bases.

📜 SIMILAR VOLUMES

Computability of compact operators on co

Computability of compact operators on computable Banach spaces with bases

✍ Vasco Brattka; Ruth Dillhage 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 210 KB

## Abstract We develop some parts of the theory of compact operators from the point of view of computable analysis. While computable compact operators on Hilbert spaces are easy to understand, it turns out that these operators on Banach spaces are harder to handle. Classically, the theory of compac

Bases in Spaces of Multilinear Forms ove

Bases in Spaces of Multilinear Forms over Banach Spaces

✍ V. Dimant; I. Zalduendo 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 217 KB

We begin by giving, in Section 1, a number of conditions including compactness and weak sequential continuity, which are equivalent to the existence of monomial bases. We apply these equivalences and the Gon-zalo᎐Jaramillo indexes to the problem of existence of monomial bases in spaces of multilinea

Some Counterexamples Concerning Strong M

Some Counterexamples Concerning Strong M-Bases of Banach Spaces

✍ M.S. Lambrou; W.E. Longstaff 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 570 KB

unconditional Bases in Banach Spaces of

unconditional Bases in Banach Spaces of Absolutely p-Summing Operators

✍ I. Schütt 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 835 KB

## Abstract In the present paper we give conditions for Banach spaces of absolutely __p__‐summing operators to have unconditional bases. In this case we obtain methods to estimate the π~__p__~‐norm. Also we consider spaces of absolutely __p__‐summing operators with “bad” structure, i.e., without lo

On Geometry of Banach Spaces with Proper

On Geometry of Banach Spaces with Property α

✍ J.P. Moreno 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 138 KB

W. Schachermayer showed that even 1-complemented subspaces of Banach spaces with property ␣ can fail this property. However, we prove in this paper that spaces with property ␣ satisfy an hereditary property. We obtain, as a conse-Ž . quence, that spaces with properties ␣ and H cannot be reflexive an

Extendible Polynomials on Banach Spaces

✍ Daniel Carando 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 114 KB

We are concerned with the following question: when can a polynomial P: Ž . E ª X E and X are Banach spaces be extended to a Banach space containing E? We prove that the polynomials that are extendible to any larger space are Ž X . precisely those which can be extended to C B , if X is complemented