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Some equivalent metrics for bounded normal operators

Mohammad Reza Jabbarzadeh, Rana Hajipouri (2018)

Mathematica Bohemica

Some stronger and equivalent metrics are defined on , the set of all bounded normal operators on a Hilbert space H and then some topological properties of are investigated.

Some new classes of topological vector spaces with closed graph theorems

Brian Rodrigues (1991)

Commentationes Mathematicae Universitatis Carolinae

In this note, we investigate non-locally-convex topological vector spaces for which the closed graph theorem holds. In doing so, we introduce new classes of topological vector spaces. Our study includes a direct extension of Pták duality to the non-locally-convex situation.

Splines and pseudo-inverses

F. J. Delvos (1978)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Subspaces with a common complement in a Banach space

Dimosthenis Drivaliaris, Nikos Yannakakis (2007)

Studia Mathematica

We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs of subspaces of a Banach space with a common complement coincide with those pairs which are isomorphic to a pair of graphs of bounded linear operators between two other Banach spaces. (2) The pairs of subspaces of a Banach space X with a common complement coincide with those pairs for which there exists an involution...

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