Cross-Gram Matrix Associated to Two Sequences in Hilbert Spaces

Ultra Bessel sequences in direct sums of Hilbert spaces

In this paper, we establish some new results in ultra Bessel sequences and ultra Bessel sequences of subspaces. Also, we investigate ultra Bessel sequences in direct sums of Hilbert spaces. <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-s...

Mixing Sequences in Hilbert Spaces

A general setup is provided for theorems of the Blum-Hanson type. Notions of strongly and weakly mixing sequences of elements in a Hubert space are defined, and equivalent characterizations are derived. It turns out that many known generalizations of the Blum-Hanson theorem are special cases of an abstract version which is also suitable for the nonlinear situation. Introduction. In [4] the noti...

ultra bessel sequences in direct sums of hilbert spaces

in this paper, we establish some new results in ultra bessel sequences and ultra bessel sequences of subspaces. also, we investigate ultra bessel sequences in direct sums of hilbert spaces.specially, we show that {( fi, gi)}∞ i=1 is a an ultra bessel sequencefor hilbert space h ⊕ k if and only if { fi}∞ i=1 and {gi}∞ i=1 are ultrabessel sequences for hilbert spaces h and k, respectively.

Ideals Associated to Two Sequences and a Matrix

Let u1×n, Xn×n, and vn×1 be matrices of indeterminates, AdjX be the classical adjoint of X, and H(n) be the ideal I1(uX)+ I1(Xv)+ I1(vu−AdjX). Vasconcelos has conjectured that H(n) is a perfect Gorenstein ideal of grade 2n. In this paper, we obtain the minimal free resolution of H(n); and thereby establish Vasconcelos’ conjecture. Let u1×n, Xn×n, and vn×1 be matrices of indeterminates over a co...

On Minimax Theory in Two Hilbert Spaces