Displaying similar documents to “Completeness of spaces wth Toeplitz decompositions”

On decomposition of k-tridiagonal ℓ-Toeplitz matrices and its applications

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.

Weak sequential completeness of sequence spaces.

Charles Swartz (1992)

Collectanea Mathematica

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Köthe and Toeplitz introduced the theory of sequence spaces and established many of the basic properties of sequence spaces by using methods of classical analysis. Later many of these same properties of sequence spaces were reestablished by using soft proofs of functional analysis. In this note we would like to point out that an improved version of a classical lemma of Schur due to Hahn can be used to give very short proofs of two of the weak sequential completeness results of Köthe...

The Mackey-Arens theorem for non-locally convex spaces.

Jerzy Kakol (1990)

Collectanea Mathematica

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Let R be a subcategory of the category of all topological vector spaces. Let E be an element of R. The problem of the existence of the finest R-topology on E with the same continuous linear functionals as the original one is discussed. Remarks concerning the Hahn-Banach Extension Property are included.