Displaying similar documents to “On the approximation numbers of large Toeplitz matrices.”

Algebras of approximation sequences: Fredholm theory in fractal algebras

Steffen Roch (2002)

Studia Mathematica

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The present paper is a continuation of [5, 7] where a Fredholm theory for approximation sequences is proposed and some of its properties and consequences are studied. Here this theory is specified to the class of fractal approximation methods. The main result is a formula for the so-called α-number of an approximation sequence (Aₙ) which is the analogue of the kernel dimension of a Fredholm operator.

Toeplitz operators and Wiener-Hopf factorisation: an introduction

M. Cristina Câmara (2017)

Concrete Operators

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Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces Hp of the upper half-plane and we review how their Fredholm properties can be studied in terms of a Wiener-Hopf factorisation of their symbols, obtaining necessary and sufficient conditions for the operator to be Fredholm or invertible, as well as formulae for their inverses or one-sided inverses when these exist. The results are applied to a...

Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices

A.K. Abdikalykov, V.N. Chugunov, Kh.D. Ikramov (2015)

Special Matrices

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Our motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices. Generalizing this result, we give a complete description of unitary similarity automorphisms of the space of Toeplitz-plus-Hankel matrices.