Light wear to spine, covers & corners. ; Memoirs of the American Mathematical Society. September 2020. Volume 267. Number 1297; 25.3 x 17.8 x 0.8cms; v. 101 pages.

Seller Inventory # LCB85251

Contact seller

Report this item

Bibliographic Details

Title: Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic S- Functional Calculus and Spectral Operators
Publisher: American Mathematical Society, Providence, Rhode Island
Publication Date: 2020
Language: English
ISBN 10: 1470442388
ISBN 13: 9781470442385
Binding: Original Wrappers
Edition: First Edition; First Impression.
Condition: Near Fine
Dust Jacket Condition: No Dust Jacket

About this title

Synopsis

"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. We show that results derived from functional calculi involving intrinsic slice functions can be formulated without the assumption of a left multiplication. We develop the S-functional calculus in this setting and also a new approach to spectral integration of intrinsic slice functions. This approach has a clear interpretation in terms of the right linear structure on the space and allows to formulate the spectral theorem without using any randomly chosen structure. The presented techniques only apply to intrinsic slice functions, but this is a negligible restriction. Indeed, due to the symmetry of the S-spectrum of T, only these functions are compatible with the very basic intuition of a functional calculus, namely that f(T) should be defined by letting f act on the spectral values of T. Using the above tools we develop a theory of spectral operators and obtain results analogue to those of the complex theory. In particular we show the existence of a canonical decomposition of a spectral operator and discuss its behavior under the S-functional calculus. Finally, we show a beautiful relation with complex operator theory: if we embed the complex numbers into the quaternions and consider the quaternionic vector space as a complex one, then complex and quaternionic operator theory are consistent. Again it is the symmetry of intrinsic slice functions that guarantees that this compatibility is true for any possible imbedding of the complex numbers"--

"About this title" may belong to another edition of this title.

Store Description

Please come visit our shop in Machynlleth or browse our stock online. We carry a wide range of academic books on all subjects, such as history, philosophy, psychology, psychiatry, mathematics, physics, geography, political science, political philosophy, religious studies, military history and many other subjects. We also carry antiquarian stock and general stock, especially cookery. We are always interested in collections, especially on academic subjects.

Visit Seller's Storefront

Association Member

Members of these associations are committed to maintaining the highest standards. They vouch for the authenticity of all items offered for sale. They provide expert and detailed descriptions, disclose all significant defects and/or restorations, provide clear and accurate pricing, and operate with fairness and honesty during the purchase experience.

Seller's business information

Literary Cat Books
United Kingdom

Sale & Shipping Terms

Terms of Sale

All orders of 50 pounds and higher will be shipped with mandatory insurance added.

We make every effort to describe each book or print accurately. However, we accept that an item might not prove to be as you expected it, or has been damaged in transport. We therefore accept returns within 14 days of receipt of the item, upon prior notification. We will provide a full refund upon receipt of the returned item by us.

Shipping Terms

Orders usually ship within 2/3 business days. Shipping costs are based on books weighing 2.2 LB, or 1 KG. If your book order is heavy or oversized, we may contact you to let you know if extra shipping is required.

Overseas postage will be sent by airmail if you select priority and surface if you select standard postage. Surface mail to the United States or Canada can take up to six weeks, and up to twelve weeks to Australia and New Zealand.

We use only good quality materials and the utmost care when packaging our books to ensure they arrive in the best possible condition.

In the unlikely event that your book does not arrive within the specified shipping period, please feel free to contact us direct. Please provide your name, address and the details of your order.