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μ - SCALE INVARIANT LINEAR RELATIONS IN HILBERT SPACES


ADRIAN SANDOVICI
Department of Sciences, University "Al. I. Cuza", Lascăr Catargi 54, 700107, Iaşi Romania, e-mail: adrian.sandovici@uaic.ro

Issue:

SSRSMI, Number 1, Volume XXI

Section:

Volume 21, Number 1

Abstract:

The concept of μ-scale invariant operator with respect to an unitary transformation in a separable Hilbert space is extended to the case of linear relations (multi-valued linear operators). It is shown that if S is a nonnegative linear relation which is μ -scale invariant for some μ>0, then its adjoint S* and its extreme selfadjoint extensions SF and SN are also μ scale invariant.

Keywords:

Hilbert space, linear relation, nonnegative selfadjoint extension, unitary transformation, scale invariant relation.

Code [ID]:

SSRSMI201101V21S01A0020 [0003422]

Full paper:

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