ℝ-orbit reflexive operators

Rank-one operators in reflexive one-sided A-submodules

In this paper, we first characterize reflexive one-sided A -submodules U of a unital operator algebra A in B(H ) completely. Furthermore we investigate the invariant subspace lattice Lat R and the reflexive hull Ref R, where R is the submodule generated by rank-one operators in U ; in particular, if L is a subspace lattice, we obtain when the rank-one algebra R of Alg L is big enough to determi...

On operators from separable reflexive spaces with asymptotic structure

Let 1 < q < p < ∞ and q ≤ r ≤ p. Let X be a reflexive Banach space satisfying a lower-lq-tree estimate and let T be a bounded linear operator from X which satisfies an upper-lp-tree estimate. Then T factors through a subspace of ( ∑ Fn)lr , where (Fn) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an (lp, lq) FDD. Similarly, let...

Image Analysis with R-operators

Associative nets is a well suited parallel computing model for image analysis. It allows to perform asynchronous computations an irregular data. Some e cient implementations have been designed, either in hardware or software. Asynchronism can largely improve the algorithm speeds, provided these algorithms can be written with operators that allow the asynchronous implementation. Classical operat...

Resolvents of R-diagonal Operators

We consider the resolvent (λ−a)−1 of any R-diagonal operator a in a II1-factor. Our main theorem (Theorem 1.1) gives a universal asymptotic formula for the norm of such a resolvent. En route to its proof, we calculate the R-transform of the operator |λ− c|2 where c is Voiculescu’s circular operator, and we give an asymptotic formula for the negative moments of |λ − a|2 for any R-diagonal a. We ...

Inner Model Operators in L(R)