scholarly journals Remarks on Essential Maximal Numerical Range of Aluthge Transform

2019 ◽  
Vol 20 ◽  
pp. 1-5
Author(s):  
Omukhwaya Sakwa Cyprian ◽  
Lucy Chikamai ◽  
Shem Aywa
Keyword(s):  
Numerical Range ◽  
Aluthge Transform ◽  
Hyponormal Operators

This paper focuses on the properties of the essential maximal numerical range of Aluthgetransform T. For instance, among other results, we show that the essential maximal numerical rangeof Aluthge transform is nonempty and convex. Further, we prove that the essential maximal numericalrange of Aluthge transform e T is contained in the essential maximal numerical range of T. This studyis therefore an extention of the research on Aluthge transform which was begun by Aluthge in hisstudy of p−hyponormal operators.

On the numerical range behavior under the generalized Aluthge transform

2008 ◽  
Vol 56 (1-2) ◽  
pp. 163-177
Author(s):  
David E. V. Rose ◽  
Ilya M. Spitkovsky
Keyword(s):  
Numerical Range ◽  
Aluthge Transform

Complex strict and uniform convexity and hyponormal operators

1984 ◽  
Vol 96 (3) ◽  
pp. 483-493 ◽  
Author(s):  
Kirsti Mattila
Keyword(s):  
Banach Space ◽  
Dual Space ◽  
Numerical Range ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Uniform Convexity ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Hyponormal Operators ◽  
Image Position

Let X be a complex Banach space. We denote by X* the dual space of X and by B(X) the space of all bounded linear operators on X. The (spatial) numerical range of an operator TεB(X) is defined as the setIf V(T) ⊂ ℝ, then T is called hermitian. More about numerical ranges may be found in [8] and [9].

scholarly journals On Relation between the Joint Essential Spectrum and the Joint Essential Numerical Range of Aluthge Transform

2021 ◽  
pp. 1-9
Author(s):  
O. S. Cyprian
Keyword(s):  
Hilbert Space ◽  
Essential Spectrum ◽  
Numerical Range ◽  
Complex Hilbert Space ◽  
Aluthge Transform

Associated with every commuting m-tuples of operators on a complex Hilbert space X is its Aluthge transform. In this paper we show that every commuting m-tuples of operators on a complex Hilbert space X and its Aluthge transform have the same joint essential spectrum. Further, it is shown that the joint essential spectrum of Aluthge transform is contained in the joint essential numerical range of Aluthge transform.

scholarly journals On numerical ranges of generalized derivations and related properties

1984 ◽  
Vol 36 (1) ◽  
pp. 134-142 ◽  
Author(s):  
Sen-Yen Shaw
Keyword(s):  
Numerical Range ◽  
Normal Operator ◽  
Linear Operators ◽  
Minimal Norm ◽  
Bounded Linear ◽  
Hyponormal Operators ◽  
Normal Operators ◽  
Schmidt Operator ◽  
The Difference ◽  
Norm Ideal

AbstractThis paper is concerned with the numerical range and some related properties of the operator Δ/ S: T → AT – TB(T∈S), where A, B are (bounded linear) operators on the normed linear spaces X and Y. respectively, and S is a linear subspace of the space ℒ (Y, X) of all operators from Y to X. S is assumed to contain all finite operators, to be invariant under Δ, and to be suitably normed (not necessarily with the operator norm). Then the algebra numerical range of Δ/ S is equal to the difference of the algebra numerical ranges of A and B. When X = Y and S = ℒ (X), Δ is Hermitian (resp. normal) in ℒ (ℒ(X)) if and only if A–λ and B–λ are Hermitian (resp. normal) in ℒ(X)for some scalar λ;if X: = H is a Hilbert space and if S is a C *-algebra or a minimal norm ideal in ℒ(H)then any Hermitian (resp. normal) operator in S is of the form Δ/ S for some Hermitian (resp. normal) operators A and B. AT = TB implies A*T = TB* are hyponormal operators on the Hilbert spaces H1 and H2, respectively, and T is a Hilbert-Schmidt operator from H2 to H1.

A remark on numerical range of semi-hyponormal operators

2010 ◽  
Vol 58 (6) ◽  
pp. 711-714 ◽  
Author(s):  
Muneo Chō ◽  
Tadasi Huruya
Keyword(s):  
Numerical Range ◽  
Hyponormal Operators

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

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