Exact sequences for generalized Toeplitz operators

Generalized Locally Toeplitz Sequences: Theory and Applications

Toeplitz transforms of Fibonacci sequences

We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.

Generalized Continuous Frames for Operators

In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ wi...

Toeplitz Operators

This article discusses Paul Halmos’s crucial work on Toeplitz operators and the consequences of that work. Mathematics Subject Classification (2000). 47B35.

Multipliers and Toeplitz Operators on Banach Spaces of Sequences

In this paper, we prove that every multiplier M (i.e. every bounded operator commuting whit the shift operator S) on a large class of Banach spaces of sequences on Z is associated to a function essentially bounded by ‖M‖ on spec(S). This function is holomorphic on ◦ spec(S), if ◦ spec(S) 6= ∅. Moreover, we give a simple description of spec(S). We also obtain similar results for Toeplitz operato...