Contractive projections and operator spaces

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

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.

Ranges of Positive Contractive Projections in Nakano Spaces

We show that in any nontrivial Nakano space X = Lp(·)(Ω, Σ, μ) with essentially bounded random exponent function p(·), the range Y = R(P ) of a positive contractive projection P is itself representable as a Nakano space LpY (·)(ΩY , ΣY , νY ), for a certain measurable set ΩY ⊆ Ω (the support of the range), a certain sub-sigma ring ΣY ⊆ Σ (with maximal element ΩY ) naturally determined by the la...

Contractive Projections and Prediction Operators

Projections in Operator Ranges

If H is a Hilbert space, A is a positive bounded linear operator on H and S is a closed subspace of H, the relative position between S and A−1(S⊥) establishes a notion of compatibility. We show that the compatibility of (A,S) is equivalent to the existence of a convenient orthogonal projection in the operator range R(A1/2) with its canonical Hilbertian structure.