Factorization of diagonally dominant operators on $L_ 1([0,1],X)$
Authors:
Kevin T. Andrews and Joseph D. Ward
Journal:
Trans. Amer. Math. Soc. 291 (1985), 789-800
MSC:
Primary 47B38; Secondary 46E40, 47A68
DOI:
https://doi.org/10.1090/S0002-9947-1985-0800263-0
MathSciNet review:
800263
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Abstract | References | Similar Articles | Additional Information
Abstract: Let $X$ be a separable Banach space. It is shown that every diagonally dominant invertible operator on ${L_1}([0, 1], X)$ can be factored uniquely as a product of an invertible upper triangular operator and an invertible unit lower triangular operator.
- William Arveson, Interpolation problems in nest algebras, J. Functional Analysis 20 (1975), no. 3, 208β233. MR 0383098, DOI https://doi.org/10.1016/0022-1236%2875%2990041-5 M. A. Barkar and I. C. Gohberg, On factorization of operators in Banach spaces, Amer. Math. Soc. Transl. 90 (1970), 103-133.
- C. de Boor, Rong Qing Jia, and A. Pinkus, Structure of invertible (bi)infinite totally positive matrices, Linear Algebra Appl. 47 (1982), 41β55. MR 672731, DOI https://doi.org/10.1016/0024-3795%2882%2990225-7
- A. S. Cavaretta Jr., W. A. Dahmen, C. A. Micchelli, and P. W. Smith, A factorization theorem for banded matrices, Linear Algebra Appl. 39 (1981), 229β245. MR 625253, DOI https://doi.org/10.1016/0024-3795%2881%2990306-2
- C. K. Chui, J. D. Ward, and P. W. Smith, Cholesky factorization of positive definite bi-infinite matrices, Numer. Funct. Anal. Optim. 5 (1982), no. 1, 1β20. MR 703114, DOI https://doi.org/10.1080/01630568208816129
- Avraham Feintuch, Factorization along nest algebras, Proc. Amer. Math. Soc. 84 (1982), no. 2, 192β194. MR 637167, DOI https://doi.org/10.1090/S0002-9939-1982-0637167-5
- I. C. Gohberg and I. A. Felβ²dman, Convolution equations and projection methods for their solution, American Mathematical Society, Providence, R.I., 1974. Translated from the Russian by F. M. Goldware; Translations of Mathematical Monographs, Vol. 41. MR 0355675
- Richard B. Holmes, Mathematical foundations of signal processing, SIAM Rev. 21 (1979), no. 3, 361β388. MR 535119, DOI https://doi.org/10.1137/1021053
- N. J. Kalton, The endomorphisms of $L_{p}(0\leq p\leq i)$, Indiana Univ. Math. J. 27 (1978), no. 3, 353β381. MR 470670, DOI https://doi.org/10.1512/iumj.1978.27.27027
- N. J. Kalton, Isomorphisms between $L_{p}$-function spaces when $p<1$, J. Functional Analysis 42 (1981), no. 3, 299β337. MR 626447, DOI https://doi.org/10.1016/0022-1236%2881%2990092-6
- David R. Larson, Nest algebras and similarity transformations, Ann. of Math. (2) 121 (1985), no. 3, 409β427. MR 794368, DOI https://doi.org/10.2307/1971180
- P. W. Smith and J. D. Ward, Factorization of diagonally dominant operators on $l_1$, Illinois J. Math. 29 (1985), no. 3, 370β381. MR 786727
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Additional Information
Keywords:
Diagonally dominant,
triangular,
invertible
Article copyright:
© Copyright 1985
American Mathematical Society