Numerical ranges of operators on normed spaces and of elements of normed algebras / F.F. Bonsall and J. Duncan.

Format:

Book

Author/Creator:

Bonsall, F. F., author.

Duncan, J. (John), 1938- author.

Series:

London Mathematical Society lecture note series ; 2.

London Mathematical Society lecture note series ; 2

Language:

English

Subjects (All):

Normed linear spaces.

Banach algebras.

Linear operators.

Physical Description:

1 online resource (ii, 142 pages) : digital, PDF file(s).

Other Title:

Numerical Ranges of Operators on Normed Spaces & of Elements of Normed Algebras

Place of Publication:

Cambridge : Cambridge University Press, 1971.

Language Note:

English

Summary:

The theory of the numerical range of a linear operator on an arbitrary normed space had its beginnings around 1960, and during the 1970s the subject has developed and expanded rapidly. This book presents a self-contained exposition of the subject as a whole. The authors develop various applications, in particular to the study of Banach algebras where the numerical range provides an important link between the algebraic and metric structures.

Contents:

Cover; Title; Copyright; Contents; Introduction; 1. Numerical Range In Unital Normed Algebras; 2. ELEMENTARY THEOREMS; 3. THE EXPONENTIAL FUNCTION; 4. NUMERICAL RADIUS THEOREMS; 2. Hermitian Elements of a Complex Unital Banach Algebra; 5. VIDAV'S LEMMA AND APPLICATIONS; 6. THE VIDAV -PALMER THEOREM; 7. APPLICATIONS OF THE VIDAV-PALMERTHEOREM TO B*-ALGEBRAS; 8. OTHER APPLICATIONS OF THE VIDA V -PALMER THEOREM; 3. Operators; 9. THE SPATIAL NUMERICAL RANGE; 10. SPECTRAL PROPERTIES; 11. GEOMETRIC AND TOPOLOGICAL PROPERTIES OF V(T); 4. Some Recent Developments

12. THE SECOND DUAL OF A BANACH ALGEBRA13. SPECTRAL STATES; 14. REMARKS AND PROBLEMS; BIBLIOGRAPHY; INDEX

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 131-137) and index.

ISBN:

1-139-88357-7

1-107-35989-9

1-4619-3814-7

1-107-29862-8

1-107-38994-1

1-107-39836-3

1-107-38712-4

1-107-39473-2

OCLC:

862614435