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
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.