Lower upper factorizations of operators with middle terms

A. Ben-Artzi; I. Gohberg

doi:10.1016/0022-1236(88)90089-4

Lower upper factorizations of operators with middle terms

A. Ben-Artzi^*
, I. Gohberg

^*Corresponding author for this work

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we consider factorizations of the form I - K = (I + K_-)(D + F)(I + K₊), where K_-, K₊, and D are lower, upper, and diagonal operators relative to a maximal chain P of orthoprojections in a separable Hilbert space. In the case when K, K_-, and K₊ are Hilbert-Schmidt, we determine the minimal rank of the operator F which occurs in the middle term of the factorization.

Original language	English
Pages (from-to)	309-325
Number of pages	17
Journal	Journal of Functional Analysis
Volume	77
Issue number	2
DOIs	https://doi.org/10.1016/0022-1236(88)90089-4
State	Published - Apr 1988

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title = "Lower upper factorizations of operators with middle terms",

abstract = "In this paper we consider factorizations of the form I - K = (I + K-)(D + F)(I + K+), where K-, K+, and D are lower, upper, and diagonal operators relative to a maximal chain P of orthoprojections in a separable Hilbert space. In the case when K, K-, and K+ are Hilbert-Schmidt, we determine the minimal rank of the operator F which occurs in the middle term of the factorization.",

author = "A. Ben-Artzi and I. Gohberg",

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AB - In this paper we consider factorizations of the form I - K = (I + K-)(D + F)(I + K+), where K-, K+, and D are lower, upper, and diagonal operators relative to a maximal chain P of orthoprojections in a separable Hilbert space. In the case when K, K-, and K+ are Hilbert-Schmidt, we determine the minimal rank of the operator F which occurs in the middle term of the factorization.

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Lower upper factorizations of operators with middle terms

Abstract

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