NUMERICAL RANGE OF OPERATORS AND STRUCTURE IN BANACH SPACES

1982 ◽  
Vol 33 (3) ◽  
pp. 357-364 ◽  
Author(s):  
R. PAYÁ-ALBERT
Keyword(s):  
Banach Spaces ◽  
Numerical Range

scholarly journals The numerical ranges of unbounded linear operators

1975 ◽  
Vol 12 (1) ◽  
pp. 23-25 ◽  
Author(s):  
Béla Bollobás ◽  
Stephan E. Eldridge
Keyword(s):  
Banach Space ◽  
Scalar Field ◽  
Banach Spaces ◽  
Unbounded Operator ◽  
Numerical Range ◽  
Linear Operators ◽  
Density Property ◽  
Unbounded Linear Operators

Giles and Joseph (Bull. Austral. Math. Soc. 11 (1974), 31–36), proved that the numerical range of an unbounded operator on a Banach space has a certain density property. They showed, in particular, that the numerical range of an unbounded operator on certain Banach spaces is dense in the scalar field. We prove that the numerical range of an unbounded operator on a Banach space is always dense in the scalar field.

Some properties of the essential numerical range on Banach spaces

2017 ◽  
Vol 6 ◽  
pp. 105-111
Author(s):  
L. N. Muhati ◽  
J. O. Bonyo ◽  
J. O. Agure
Keyword(s):  
Banach Spaces ◽  
Numerical Range

scholarly journals On the essential numerical spectrum of operators on Banach spaces

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 2191-2199
Author(s):  
Bouthaina Abdelhedi ◽  
Wissal Boubaker ◽  
Nedra Moalla
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Numerical Range

The purpose of this paper is to define and develop a new notion of the essential numerical spectrum ?en(.) of an operator on a Banach space X and to study its properties. Our definition is closely related to the essential numerical range We(.).

scholarly journals Numerical ranges of conjugations and antilinear operators on a Banach space

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2715-2720
Author(s):  
Muneo Chō ◽  
Injo Hur ◽  
Ji Lee
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Unit Circle ◽  
Banach Spaces ◽  
Unit Disc ◽  
Numerical Range ◽  
Space Setting ◽  
Path Connectedness ◽  
The Given

In this paper, we prove that the numerical range of a conjugation on Banach spaces, using the connected property, is either the unit circle or the unit disc depending the dimension of the given Banach space. When a Banach space is reflexive, we have the same result for the numerical range of a conjugation by applying path-connectedness which is applicable to the Hilbert space setting. In addition, we show that the numerical ranges of antilinear operators on Banach spaces are contained in annuli.

scholarly journals Fixed points of holomorphic mappings for domains in Banach spaces

2003 ◽  
Vol 2003 (5) ◽  
pp. 261-274 ◽  
Author(s):  
Lawrence A. Harris
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Holomorphic Function ◽  
Fixed Points ◽  
Banach Spaces ◽  
Point Theorem ◽  
Numerical Range ◽  
Holomorphic Functions ◽  
Holomorphic Mappings

We discuss the Earle-Hamilton fixed-point theorem and show how it can be applied when restrictions are known on the numerical range of a holomorphic function. In particular, we extend the Earle-Hamilton theorem to holomorphic functions with numerical range having real part strictly less than 1. We also extend the Lumer-Phillips theorem estimating resolvents to dissipative holomorphic functions.

scholarly journals Joint spectra and joint numerical ranges for pairwise commuting operators in Banach spaces

1988 ◽  
Vol 30 (2) ◽  
pp. 145-153 ◽  
Author(s):  
Volker Wrobel
Keyword(s):  
Banach Space ◽  
Convex Hull ◽  
Banach Algebra ◽  
Banach Spaces ◽  
Numerical Range ◽  
Linear Operators ◽  
Continuous Linear ◽  
Joint Spectrum ◽  
Commuting Operators ◽  
Continuous Linear Operators

In a recent paper M. Cho [5] asked whether Taylor's joint spectrum σ(a1, …, an; X) of a commuting n-tuple (a1,…, an) of continuous linear operators in a Banach space X is contained in the closure V(a1, …, an; X)- of the joint spatial numerical range of (a1, …, an). Among other things we prove that even the convex hull of the classical joint spectrum Sp(a1, …, an; 〈a1, …, an〉), considered in the Banach algebra 〈a1, …, an〉, generated by a1, …, an, is contained in V(a1, …, an; X)-.

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