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Lipschitz algebras

✍ Scribed by Nik Weaver

Book ID
127418657
Publisher
World Scientific
Year
1999
Tongue
English
Weight
2 MB
Edition
1st
Category
Library
City
River Edge, NJ
ISBN-13
9789810238735

No coin nor oath required. For personal study only.

✦ Synopsis

The Lipschitz algebras Lp(M), for M a complete metric space, are quite analogous to the spaces C() and L(X), for a compact Hausdorff space and X a -finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.

πŸ“œ SIMILAR VOLUMES

Approximation in Lipschitz algebras
Approximation in Lipschitz algebras
✍ Honary, T.G.; Mahyar, H. πŸ“‚ Article πŸ“… 2000 πŸ› Taylor and Francis Group 🌐 English βš– 157 KB
Order Completeness in Lipschitz Algebras
Order Completeness in Lipschitz Algebras
✍ N. Weaver πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 530 KB

The algebraic properties of Lipschitz spaces have received much attention. This has led to a good understanding of such things as complex homomorphisms and ideals (but not subalgebras) when the underlying metric space is compact. Taking a cue from the recent observation that Lipschitz spaces are ord

Automatic Continuity of Lipschitz Algebr
Automatic Continuity of Lipschitz Algebras
✍ B. Pavlovic πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 980 KB

For a compact metric space \((K, d), \alpha \in(0,1]\) and \(f \in C(K)\), let \(p_{x}(f)=\) \(\sup \left\{|f(t)-f(s)| d(t, s)^{x}: t, s \in K\right\}\). The set \(\operatorname{Lip}_{x}(K, d)=\left\{f \in C(K): p_{x}(f)<\infty\right\}\) with the norm \(\|f\|_{x}=|f|_{\kappa}+p_{x}(f)\) is a Banach

Discontinuous Maps from Lipschitz Algebr
Discontinuous Maps from Lipschitz Algebras
✍ Branka Pavlovic πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 340 KB

For an infinite compact metric space (X, d), : # (0, 1) and f # C(X), let p Both Lip : (X, d ) and lip : (X, d ) are called Lipschitz algebras. We solve the problem of existence of homomorphisms and derivations from lip : (X, d ) which are discontinuous on every dense subalgebra. In order to achiev