On the Expectation of Operator Norms of Random Matrices

Further inequalities for operator space numerical radius on 2*2 operator ‎matrices

‎We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$‎, ‎when $X$ is a numerical radius operator space‎. ‎These inequalities contain some upper and lower bounds for operator space numerical radius.

Operator-valued Free Fisher Information of Random Matrices

We study the operator-valued free Fisher information of random matrices in an operator-valued noncommutative probability space. We obtain a formula for Φ M2(B) (A,A,M2(B), η), where A ∈ M2(B) is a 2 × 2 operator matrix on B, and η is linear operators on M2(B). Then we consider a special setting: A is an operator-valued semicircular matrix with conditional expectation covariance, and find that Φ...

A Note on Weighted Composition Operators on L^p-Spaces

The norm of polynomials in large random and deterministic matrices

Let XN = (X (N) 1 , . . . , X (N) p ) be a family of N × N independent, normalized random matrices from the Gaussian Unitary Ensemble. We state sufficient conditions on matrices YN = (Y (N) 1 , . . . , Y (N) q ), possibly random but independent of XN , for which the operator norm of P (XN ,YN ,Y∗ N) converges almost surely for all polynomials P . Limits are described by operator norms of object...

CONDITIONAL EXPECTATION IN THE KOPKA'S D-POSETS

The notion of a $D$-poset was introduced in a connection withquantum mechanical models. In this paper, we introduce theconditional expectation of  random variables on theK^{o}pka's $D$-Poset and prove the basic properties ofconditional expectation on this  structure.