### Köthe-Toeplitz Duals of some new Sequence Spaces and Their Matrix Maps

Z.U. Ahmad, Mursaleen (1987)

Publications de l'Institut Mathématique

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Z.U. Ahmad, Mursaleen (1987)

Publications de l'Institut Mathématique

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A. Ohashi, T. Sogabe, T.S. Usuda (2015)

Special Matrices

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We consider a k-tridiagonal ℓ-Toeplitz matrix as one of generalizations of a tridiagonal Toeplitz matrix. In the present paper, we provide a decomposition of the matrix under a certain condition. By the decomposition, the matrix is easily analyzed since one only needs to analyze the small matrix obtained from the decomposition. Using the decomposition, eigenpairs and arbitrary integer powers of the matrix are easily shown as applications.

Yousong Luo, Robin Hill (2015)

Special Matrices

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In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices,...

Sanzheng Qiao (1988)

Numerische Mathematik

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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.

Il'in, S.N. (2004)

Zapiski Nauchnykh Seminarov POMI

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Titus Hilberdink (2006)

Acta Arithmetica

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D.R. Sweet (1984)

Numerische Mathematik

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Yufeng Lu, Linghui Kong (2014)

Studia Mathematica

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We first determine when the sum of products of Hankel and Toeplitz operators is equal to zero; then we characterize when the product of a Toeplitz operator and a Hankel operator is a compact perturbation of a Hankel operator or a Toeplitz operator and when it is a finite rank perturbation of a Toeplitz operator.

Tadeusz Rojek (1989)

Compositio Mathematica

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D.R. Sweet (1990/91)

Numerische Mathematik

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Antosik, P., Srinivasan, V.K. (1987)

International Journal of Mathematics and Mathematical Sciences

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Huckle, Thomas K., Noutsos, Dimitrios (2007)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

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