عنوان

Spear operators between Banach spaces /

(Number (ISBN

3319713337

(Number (ISBN

9783319713335

Erroneous ISBN

3319713329

Erroneous ISBN

9783319713328

Title Proper

Spear operators between Banach spaces /

General Material Designation

[Book]

First Statement of Responsibility

Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez.

Place of Publication, Distribution, etc.

Cham, Switzerland :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2018.

Specific Material Designation and Extent of Item

1 online resource (xv, 164 pages) :

Other Physical Details

color illustrations

Series Title

Lecture notes in mathematics,

Volume Designation

2205

ISSN of Series

0075-8434 ;

Text of Note

Includes bibliographical references and index.

Text of Note

Historical Introduction: A Walk on the Results for Banach Spaces with Numerical Index 1 -- Spear Vectors and Spear Sets -- Three Definitions for Operators: Spearness, the Alternative Daugavet Property, and Lushness -- Some Examples in Classical Banach Spaces -- Further Results -- Isometric and Isomorphic Consequences -- Lipschitz Spear Operators -- Some Stability Results -- Open Problems -- Erratum to: Spear Operators Between Banach Spaces.

0

Text of Note

His monograph is devoted to the study of spear operators, that is, bounded linear operators $G$ between Banach spaces $X$ and $Y$ satisfying that for every other bounded linear operator $T:X\longrightarrow Y$ there exists a modulus-one scalar $\omega$ such that $\|G + \omega\, T\|=1+ \|T\|$. This concept extends the properties of the identity operator in those Banach spaces having numerical index one. Many examples among classical spaces are provided, being one of them the Fourier transform on $L_1$. The relationships with the Radon-Nikodým property, with Asplund spaces and with the duality, and some isometric and isomorphic consequences are provided. Finally, Lipschitz operators satisfying the Lipschitz version of the equation above are studied. The book could be of interest to young researchers and specialists in functional analysis, in particular to those interested in Banach spaces and their geometry. It is essentially self-contained and only basic knowledge of functional analysis is needed.--Provided by publisher.

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9783319713335

Title

Spear operators between Banach spaces.

International Standard Book Number

9783319713328

Banach spaces.

Operator theory.

Banach spaces.

Calculus & mathematical analysis.

Mathematics-- Mathematical Analysis.

Operator theory.

Number

Edition

Class number

Kadet︠s︡, V. M., (Vladimir M.)

Martín, Miguel, (Martín Suárez)

Merí, Javier

Pérez, Antonio, (Pérez Hernández),1989-

Date of Transaction

20200823103228.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y