Fredholm theory in topological vector spaces Dorina Mitrea, Irina Mitrea, Marius Mitrea, Joel H. Shapiro

Format:

Book

Author/Creator:

Mitrea, Dorina, 1965- author.

Mitrea, Irina, author.

Mitrea, Marius, author.

Shapiro, Joel H., author.

Series:

Springer monographs in mathematics 2196-9922

Springer Monographs in Mathematics 2196-9922

Language:

English

Subjects (All):

Fredholm operators.

Linear topological spaces.

Physical Description:

1 online resource

Place of Publication:

Cham Springer 2026

Summary:

This book aims to investigate how Riesz and Fredholm operator theories extend and adapt within the framework of topological vector spaces. At its core, this book seeks to generalize classical operator theory, traditionally developed in Banach and Hilbert spaces, to more inclusive topological settings. It offers a unified and comprehensive approach to understanding Riesz and Fredholm theories beyond the confines of local convexity and in the absence of an abundance of continuous linear functionals (which are the prevalent assumptions in existing literature). The exposition begins with foundational concepts in topology, including open and closed sets, neighborhoods, and compactness. It then introduces metrics, norms, and completeness, followed by a treatment of vector spaces, subspaces, and linear topological structures. The discussion progresses to inner products, orthogonality, and Hilbert space geometry. The heart of the book is the development of Riesz theory in topological vector spaces, beginning with compact operators, eigenvalues, and eigensubspaces, and advancing to spectral theory. This sets the stage for constructing a Fredholm theory in general topological contexts, requiring new definitions and a thorough exploration of the Fredholm index, its stability, and its applications. The book also includes a wide range of exercises (from foundational proofs to advanced problems) designed to reinforce the content covered and to provide additional insights

Contents:

Topologic,Algebraic,andFunctionalAnalyticTools

RieszTheoryinTopologicalVectorSpaces

FredholmTheoryinTopologicalVectorSpaces

Notes:

Online resource; title from PDF title page (SpringerLink, viewed April 30, 2026)

ISBN:

9783032247384

3032247381

OCLC:

1587455592

Access Restriction:

Restricted for use by site license