Some reiteration results for interpolation methods defined by means of polygons

2008 ◽  
Vol 138 (6) ◽  
pp. 1179-1195 ◽  
Author(s):  
Fernando Cobos ◽  
Luz M. Fernández-Cabrera ◽  
Joaquim Martín
Keyword(s):  
Banach Algebras ◽  
Function Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
The Real ◽  
Interpolation Methods ◽  
Real Method

We continue the research on reiteration results between interpolation methods associated to polygons and the real method. Applications are given to N-tuples of function spaces, of spaces of bounded linear operators and Banach algebras.

scholarly journals Hypo-q-Norms on Cartesian Products of Algebras of Bounded Linear Operators on Hilbert Spaces

2017 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Cartesian Product ◽  
Schwarz Inequality ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Cartesian Products ◽  
Bounded Linear ◽  
The Real ◽  
Inner Products ◽  
Reverse Inequalities

In this paper we introduce the hypo-q-norms on a Cartesian product of algebras of bounded linear operators on Hilbert spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given. Several bounds for the norms δp, ϑp and the real norms ηr,p and θr,p are provided as well.

scholarly journals The perturbation theory for the Drazin inverse and its applications II

2001 ◽  
Vol 70 (2) ◽  
pp. 189-198 ◽  
Author(s):  
Vladimir Rakočevič ◽  
Yimin Wei
Keyword(s):  
Banach Space ◽  
Perturbation Theory ◽  
Banach Algebras ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Generalized Drazin Inverse

AbstractWe study the perturbation of the generalized Drazin inverse for the elements of Banach algebras and bounded linear operators on Banach space. This work, among other things, extends the results obtained by the second author and Guorong Wang on the Drazin inverse for matrices.

scholarly journals OPERATORS ON BANACH ALGEBRA VALUED FUNCTION SPACES

1992 ◽  
Vol 23 (3) ◽  
pp. 233-238
Author(s):  
JOR-TING CHAN
Keyword(s):  
Banach Algebra ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Function Spaces ◽  
Linear Operators ◽  
Locally Compact ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Locally Compact Hausdorff Space

Let $S$ be a locally compact Hausdorff space and let $A$ be a Banach algebra. Denote by $C_0(S, A)$ the Banach algebra of all $A$-valued continuous functions vanishing at infinity on $S$. Properties of bounded linear operators on $C_0(S,A)$, like multiplicativity, are characterized by Choy in terms of their representing measures. We study these theorems and give sharper results in certain cases.

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

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