6 papers
Model Theory for Operators Related to Square Roots of Normal Operators
Raul E. Curto, Thankarajan Prasad
In this paper we prove that a square root of a cyclic normal operator is unitarily equivalent to a block multiplication operator on a vector-valued Lebesgue space with a --norma…
Hyponormal block Toeplitz operators with finite rank self-commutators
Mankunikuzhiyil Abhinand, Raul E. Curto, Thankarajan Prasad
In this paper, we identify a large class of hyponormal block Toeplitz operators whose self-commutators are of finite rank. \ Recall that an operator is hyponormal and $[T_Ï…
Semi-hyponormality of commuting pairs of Hilbert space operators
Raul E. Curto, Jasang Yoon
We first find an explicit formula for the square root of positive operator matrices with commuting entries, and then use it to define and study semi-hyponormality for…
Propagation Phenomena for Operator-Valued Weighted Shifts
Raul E. Curto, Abderrazzak Ech-charyfy, Hamza El Azhar +1
This paper is devoted to the study of propagation phenomena for --hyponormal, quadratically hyponormal, and cubically hyponormal operator-valued weighted shifts. \ First, we sho…
A Combinatorial Formula for Recursive Operator Sequences and Applications
Raul E. Curto, Abderrazzak Ech-charyfy, Kaissar Idrissi +1
We study sequences of bounded operators \((T_n)_{n \ge 0}\) on a complex separable Hilbert space \(\mathcal{H}\) that satisfy a linear recurrence relation of the form $$ T_{n+r} =…
The Square Root Problem and Subnormal Aluthge Transforms of Recursively Generated Weighted Shifts
Raul E. Curto, Hamza El Azhar, Youssef Omari +1
For recursively generated shifts, we provide definitive answers to two outstanding problems in the theory of unilateral weighted shifts: the Subnormality Problem ({\bf SP}) (relate…