Factorization of diagonally dominant operators on 𝐿₁([0,1],𝑋)

Andrews, Kevin T.; Ward, Joseph D.

doi:10.1090/S0002-9947-1985-0800263-0

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: 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, 208–233. 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), 41–55. 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), 229–245. 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, 1–20. MR 703114, DOI https://doi.org/10.1080/01630568208816129
Avraham Feintuch, Factorization along nest algebras, Proc. Amer. Math. Soc. 84 (1982), no. 2, 192–194. MR 637167, DOI https://doi.org/10.1090/S0002-9939-1982-0637167-5
I. C. Gohberg and I. A. Fel′dman, 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, 361–388. 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, 353–381. 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, 299–337. 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, 409–427. 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, 370–381. MR 786727