Leo Livshits

An irreducible semigroup of non-negative square-zero operators

We construct an irreducible multiplicative semigroup of non-negative square-zero operators acting onLp[0,1), for 1≤p<∞.

A note on 0-1 Schur multipliers

Abstract We answer a question of Q. Stout about the role of the triangular truncation in constructing 0-1 matrices that are not Schur multipliers. We also demonstrate that the triangular truncation on M2 has the third smallest norm (after 0 and 1) that any map induced by a 0-1 Schur multiplier can have.

Banach space duality of absolute Schur algebras

Matrix Schur product is the entry-wise product of matrices of the same size. It was shown by P. Chaisuriya and S.-C. Ong [1] that (forr≥1) infinite matrices [ajk] such that [|ajk|r] ɛB(l2 form a Banach algebra under the norm ‖[ajk]‖r=‖[|ajk|r]‖1/r and the Schur product. In this paper we demonstrate the existence of Banach space duality within the class of these algebras which is analogous to the classical duality between the spaces of compact, trace class, and bounded operators onl2. Also we obtain a general functional calculus on these algebras, which is used to determine the spectrum and to justify the notion of ∞-norm introduced in [1].

On transitive linear semigroups

Abstract This paper deals with semigroups of linear transformations which act transitively on a finite-dimensional vector space. An explicit canonical form is obtained for the semigroups which lack proper transitive left ideals. The class of such semigroups can be considered to be an extention of the class of transitive groups. It contains all minimal transitive (and hence all sharply transitive) semigroups.

Groups of Matrices That Act Monopotently

In the present article, the authors continue the line of inquiry started by Cigler and Jerman, who studied the separation of eigenvalues of a matrix under an action of a matrix group. The authors consider groups \Fam{G} of matrices of the form

A spatial version of Wedderburn’s Principal Theorem

\left[\small{\begin{smallmatrix} G & 0\\ 0& z \end{smallmatrix}}\right]

MULTIPLICATIVE DIAGONALS OF MATRIX SEMIGROUPS

, where

Operator Semigroups for which Reducibility Implies Decomposability

z

n-Transitivity and the complementation property

is a complex number, and the matrices

Cone-transitive matrix semigroups

G