Titlebook: Banach Space Theory; The Basis for Linear Marián Fabian,Petr Habala,Václav Zizler Textbook 2011 Springer Science+Business Media, LLC 2011 R

falsehood

Higher Order Smoothness,In this chapter, we will first discuss the properties of smoothness in .. spaces and in Hilbert spaces. Then we study spaces that have countable James boundary in connection with their higher order smoothness, and its applications. In particular, we study spaces of continuous functions on countable compact spaces.

AMPLE

Topics in Weak Topologies on Banach Spaces,In this chapter we study the weak and weak. topologies of Banach spaces in more detail. We discuss several types of compacta (Eberlein, uniform Eberlein, scattered, Corson, and more), weakly Lindelöf determined spaces and properties of tightness in weak topologies. We discuss some applications in the structural properties of some Banach spaces.

invulnerable

Tensor Products,This chapter is an introduction to the topological theory of tensor products of Banach spaces. The focus lies on the applications of tensors in the duality theory for spaces of operators, and their structure as Banach spaces. We discuss the role of the approximation property and Enflo’s example of a Banach space without the approximation property.

Infant

Habituate

Incisor

Obsessed

Structure of Banach Spaces,tability of .. in separable overspaces, lifting property of .. and Pełczyński’s characterization of separable Banach spaces containing ... We present Rosenthal’s .. theorem, Odell–Rosenthal theorem and the Rosenthal–Bourgain–Fremlin–Talagrand theory of Baire-1 functions on Polish spaces.

无能的人

Finite-Dimensional Spaces,of the local theory of Banach spaces. It is a vast and deep part of Banach space theory intimately related to probability and combinatorics. Our goal is to familiarize the reader with some of its basic notions and results that are accessible without the use of deep probabilistic tools.

粗俗人

,,-Smoothness in Separable Spaces,ns, in particular by means of ..-smooth renormings and differentiability properties of convex functions. Asplund spaces also play an important role in applications. We study basic results in smooth approximation and ranges of smooth nonlinear operators.

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