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Banach space

Overview page. Subjects: Mathematics.

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

See overview in Oxford Index

Spectral Theory for Noncommuting Operators

Gerald W. Johnson, Michel L. Lapidus and Lance Nielsen.

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

Gerald W. Johnson, Michel L. Lapidus and Lance Nielsen.

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

Gerald W. Johnson, Michel L. Lapidus and Lance Nielsen.

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

Gerald W Johnson, Michel L. Lapidus and Lance Nielsen.

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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