Result: Invariance Properties of Thematic Factorizations of Matrix Functions: Invariance properties of thematic factorizations of matrix functions
Title:
Invariance Properties of Thematic Factorizations of Matrix Functions: Invariance properties of thematic factorizations of matrix functions
Authors:
Source:
Journal of Functional Analysis. 179:309-332
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 2001.
Publication Year:
2001
Subject Terms:
Linear operator approximation theory, superoptimal approximation, Mathematics - Complex Variables, 47B35, 46E15, 30D55, residual entry, badly approximable matrix function, monotone thematic factorization, 01 natural sciences, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones), Functional Analysis (math.FA), Mathematics - Functional Analysis, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Complex Variables (math.CV), 0101 mathematics, Analysis
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0022-1236
DOI:
10.1006/jfan.2000.3667
DOI:
10.48550/arxiv.math/0101182
Access URL:
Rights:
Elsevier Non-Commercial
arXiv Non-Exclusive Distribution
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....055a64a4d06c9ee39e56711a0363fafc
Database:
OpenAIRE
Further Information
We study the problem of invariance of indices of thematic factorizations. Such factorizations were introduced in [PY1] for studying superoptimal approximation by bounded analytic matrix functions. As shown in [PY1], the indices may depend on the choice of a thematic factorization. We introduce the notion of a monotone thematic factorization. The main result shows that under natural assumptions a matrix function that admits a thematic factorization also admits a monotone thematic factorization and the indices of a monotone thematic factorization are uniquely determined by the matrix function itself. We obtain similar results for so-called partial thematic factorizations.
20 pages