We show that a Jordan algebra of compact quasinilpotent operators which contains a nonzero trace class operator has a common invariant subspace. As a consequence of this result, we obtain that a Jordan algebra of quasinilpotent Schatten operators is simultaneously triangularizable.

A weighted mean matrix, denoted by (N , pn), is a lower triangular matrix with entries pk/Pn, where {pk} is a nonnegative sequence with p0 > 0, and Pn := ∑n k=0 pk. Mishra and Srivastava [1] obtained sufficient conditions on a sequence {pk} and a sequence {λn} for the series ∑ anPnλn/npn to be absolutely summable by the weighted mean matrix (N , pn). Bor [2] extended this result to absolute sum...

Aweighted mean matrix, denoted by N,pn , is a lower triangular matrix with entries pk/Pn, where {pk} is a nonnegative sequence with p0 > 0, and Pn : ∑n k 0 pk. Mishra and Srivastava 1 obtained sufficient conditions on a sequence {pk} and a sequence {λn} for the series ∑ anPnλn/npn to be absolutely summable by the weighted mean matrix N,pn . Recently Savaş and Rhoades 2 established the correspon...

In this paper, we first consider n × n upper-triangular matrices with entries in a given semiring k. Matrices of this form with invertible diagonal entries form a monoid Bn(k). We show that Bn(k) splits as a semidirect product of the monoid of unitriangular matrices Un(k) by the group of diagonal matrices. When the semiring is a field, Bn(k) is actually a group and we recover a well-known resul...

Let G be the group of n×n upper-triangular matrices with elements in a finite field and ones on the diagonal. This paper applies the character theory of Andre, Carter and Yan to analyze a natural random walk based on adding or subtracting a random row from the row above.

Let T be an operator-weighted shift whose weights are 2-by-2 matrices. We say that, given > 0, T is in the -canonical form if each weight is an upper triangular matrix (aij), with 0 ≤ a11, a22 ≤ 1 and a12 6= 0 implies a11, a22 < . We generalize this concept to operator-weighted shifts whose weights are n-by-n matrices and we show that every polynomially bounded weighted shift, whose weights are...

Let A be a local commutative principal ideal ring. We study the double coset space of GLn(A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of A. We introduce some invariants of the double cosets. If k is the length of the ring, we determine for which of the pairs (n, k) the dou...

We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices.

Generators are found for the field of invariants of coadjoint representations for the Lie algebras that are factors of a unitriangular Lie algebra by some regular ideal.

An m by n sign pattern A is an m by n matrix with entries in {+,−, 0}. The sign pattern A requires a positive (resp. nonnegative) left inverse provided each real matrix with sign pattern A has a left inverse with all entries positive (resp. nonnegative). In this paper, necessary and sufficient conditions are given for a sign pattern to require a positive or nonnegative left inverse. It is also ...