Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space V . This has technical reasons, as the space of bounded operators on V is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.

Operator Theory on One-sided Quaternion Linear Spaces: Intrinsic S-functional Calculus and Spectral Operators (Memoirs of the American Mathematical Society)

Science & Math

Gantner, Jonathan

Mathematics

Amer Mathematical Society

Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes (Operator Theory: Advances and Applications, 274)

This book presents a new theory for evolution operators and a new method for defining fractional powers of vector operators. This new approach allows to define new classes of fractional diffusion and evolution problems. These innovative methods and techniques, based on the concept of S-spectrum, can inspire researchers from various areas of operator theory and PDEs to explore new research directions in their fields.This monograph is the natural continuation of the book: Spectral Theory on the S-Spectrum for Quaternionic Operators by Fabrizio Colombo, Jonathan Gantner, and David P. Kimsey  (Operator Theory: Advances and Applications, Vol. 270).

Colombo, Fabrizio

Evolution

Birkhauser

This book presents a new theory for evolution operators and a new method for defining fractional powers of vector operators.&nbsp;This new approach allows to define new classes of fractional diffusion and evolution problems.&nbsp; These innovative methods and techniques, based on the concept of S-spectrum,&nbsp;can inspire researchers from various areas of operator theory and PDEs&nbsp;to explore new research directions in their fields. This monograph is the natural continuation of the book: Spectral Theory on the S-Spectrum for Quaternionic Operators by Fabrizio Colombo, Jonathan Gantner, and David P. Kimsey&nbsp; (Operator Theory: Advances and Applications, Vol. 270).

See the best price to sell, buy, or rent books by Gantner, Jonathan. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Gantner, Jonathan

See the best price to sell, buy, or rent books by Gantner, Jonathan. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Operator Theory on One-sided Quaternion Linear Spaces: Intrinsic S-functional Calculus and Spectral Operators (Memoirs of the American Mathematical Society)

Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes (Operator Theory: Advances and Applications, 274)

Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes (Operator Theory: Advances and Applications, 274)