## Banach space

Overview page. Subjects: Mathematics.

A complete normed vector space on the real or complex numbers.

## Spectral Theory for Noncommuting Operators

in** Feynman's Operational Calculus and Beyond**

August 2015; p ublished online September 2015 .

Chapter. Subjects: Mathematical and Statistical Physics; Mathematics. 9320 words.

This chapter, on spectral theory for noncommuting operators, seeks to extend the operational calculus beyond the setting of the analytic functions in the disentangling algebra. When the...

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## Disentangling: Definitions, Properties and Elementary Examples

in** Feynman's Operational Calculus and Beyond**

August 2015; p ublished online September 2015 .

Chapter. Subjects: Mathematical and Statistical Physics; Mathematics. 20736 words.

A rigorous approach to Feynman’s operational calculus, the formation of functions of several noncommuting operators, is introduced, using Feynman’s heuristic “rules” as a guide. Two...

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## Disentangling via Tensor Products and Ordered Supports

in** Feynman's Operational Calculus and Beyond**

August 2015; p ublished online September 2015 .

Chapter. Subjects: Mathematical and Statistical Physics; Mathematics. 20732 words.

More involved types of disentanglings are considered in this chapter. We discuss the situation where the Banach space *X* can be written as a direct sum X=Y⊕Z, for some Banach spaces *Y* and Z,...

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## Feynman's Operational Calculus and Beyond

August 2015; p ublished online September 2015 .

Book. Subjects: Mathematical and Statistical Physics; Mathematics. 384 pages.

This book provides an abstract theory of Feynman’s operational calculus for functions of (typically) noncommuting operators. Although it is inspired by Feynman’s original heuristic...

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