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ORTHOGONALITY AND PARALLELISM OF OPERATORS ON VARIOUS BANACH SPACES

Part of: General theory of linear operators

Published online by Cambridge University Press:  22 August 2018

T. BOTTAZZI ,
C. CONDE ,
M. S. MOSLEHIAN ,
P. WÓJCIK  and
A. ZAMANI
T. BOTTAZZI
Affiliation:
Instituto Argentino de Matemática, ‘Alberto P. Calderón’, Saavedra 15 3o piso, (C1083ACA) Buenos Aires, Argentina email tpbottaz@ungs.edu.ar
C. CONDE
Affiliation:
Instituto Argentino de Matemática, ‘Alberto P. Calderón’, Saavedra 15 3o piso, (C1083ACA) Buenos Aires, Argentina Instituto de Ciencias, Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, (B1613GSX) Los Polvorines, Argentina email cconde@ungs.edu.ar
M. S. MOSLEHIAN*
Affiliation:
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran email moslehian@um.ac.ir
P. WÓJCIK
Affiliation:
Institute of Mathematics, Pedagogical University of Cracow, Podchora̧żych 2, 30-084 Kraków, Poland email pwojcik@up.krakow.pl
A. ZAMANI
Affiliation:
Department of Mathematics, Farhangian University, Tehran, Iran email zamani.ali85@yahoo.com
*
✉moslehian@um.ac.ir
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Abstract

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We present some properties of orthogonality and relate them with support disjoint and norm inequalities in $p$-Schatten ideals. In addition, we investigate the problem of characterization of norm-parallelism for bounded linear operators. We consider the characterization of the norm-parallelism problem in $p$-Schatten ideals and locally uniformly convex spaces. Later on, we study the case when an operator is norm-parallel to the identity operator. Finally, we give some equivalence assertions about the norm-parallelism of compact operators. Some applications and generalizations are discussed for certain operators.

Keywords

orthogonality; norm-parallelism; Schatten p-norm; disjoint supports; trace; compact operator

MSC classification

Primary: 47A30: Norms (inequalities, more than one norm, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 106 , Issue 2 , April 2019 , pp. 160 - 183
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The third author was supported by a grant from Ferdowsi University of Mashhad (no. 1/43523).

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