Abstract view
Exact and Approximate Operator Parallelism


Published:20140926
Printed: Mar 2015
Mohammad Sal Moslehian,
Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad 91775, Iran
Ali Zamani,
Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad 91775, Iran
Abstract
Extending the notion of parallelism we introduce the concept of
approximate parallelism in normed spaces and then substantially
restrict ourselves to the setting of Hilbert space operators endowed
with the operator norm. We present several characterizations of the
exact and approximate operator parallelism in the algebra
$\mathbb{B}(\mathscr{H})$ of bounded linear operators acting on a
Hilbert space $\mathscr{H}$. Among other things, we investigate the
relationship between approximate parallelism and norm of inner
derivations on $\mathbb{B}(\mathscr{H})$. We also characterize the
parallel elements of a $C^*$algebra by using states. Finally we
utilize the linking algebra to give some equivalence assertions
regarding parallel elements in a Hilbert $C^*$module.
MSC Classifications: 
47A30, 46L05, 46L08, 47B47, 15A60 show english descriptions
Norms (inequalities, more than one norm, etc.) General theory of $C^*$algebras $C^*$modules Commutators, derivations, elementary operators, etc. Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]
47A30  Norms (inequalities, more than one norm, etc.) 46L05  General theory of $C^*$algebras 46L08  $C^*$modules 47B47  Commutators, derivations, elementary operators, etc. 15A60  Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]
