Contractive projections and prediction operators

Contractive Projections and Prediction Operators

Contractive Projections on Banach Spaces

Increasing sequences of contractive projections on a reflexive LP space share an unconditionality property similar to that exhibited sequences of self-adjoint projections on a Hilbert space. A slight variation of this property is shown to be precisely the correct condition on a reflexive Banach space to ensure that every operator with a contractive AC-functional calculus is scalar-type spectraL

Commuting Contractive Operators

We proved that a finite commuting Boyd-Wong type contractive family with equicontinuous words have the approximate common fixed point property. We also proved that given X Ă R, compact and convex subset, F : X Ñ X a compact-and-convex valued Lipschitz correspondence and g an isometry on X, then gF “ F g implies F admits a Lipschitz selection commuting with g.

Images of contractive projections on operator algebras

It is shown that if P is a weak∗-continuous contractive projection on a JBW∗-triple M , then P(M) is of type I or semifinite, respectively, if M is of the corresponding type. We also show that P(M) has no infinite spin part if M is a type I von Neumann algebra.  2002 Elsevier Science (USA). All rights reserved.

Common fixed points of quasi-contractive operators

We establish a general theorem to approximate common fixed points of quasi-contractive operators on a normed space through the modified Ishikawa iteration process with errors in the sense of Liu [8]. Our result generalizes and improves upon, among others, the corresponding result of Berinde [1]. 2000 Mathematical Subject Clasification: Primary 47H10, 47H17: Secondary 54H25