Title of article :
On Some Properties of K-g-Riesz Bases in Hilbert Spaces
Author/Authors :
Shekari, Azam Department of Mathematics - Faculty of Sciences - University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran , Abdollahpour, Mohammad Reza Department of Mathematics - Faculty of Sciences - University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
Abstract :
In this paper, we study the K-Riesz bases and the K-g-Riesz bases in Hilbert spaces. We show that for K 2 B(H), a KRiesz basis is precisely the image of an orthonormal basis under a bounded left-invertible operator such that the range of this operator includes the range of K. Also, we show that fi 2 B(H;Hi) : i 2 Ig is a K-g-Riesz basis for H with respect to fHigi2I if and only if there exists a g-orthonormal basis fQigi2I
for H and a bounded right-invertible operator U on H such that i = QiU for all i 2 I, and R(K) R(U).
Keywords :
K-Riesz basis , K-g-Riesz basis , Right-invertible
Journal title :
Wavelets and Linear Algebra
