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Hermitian solutions to the system of operator equations TiX = Ui
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نویسنده
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bakhtiari zahra ,vaezpour s. mansour ,ebadian ali
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منبع
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international journal of nonlinear analysis and applications - 2019 - دوره : 10 - شماره : 1 - صفحه:139 -152
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چکیده
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In this article we consider the system of operator equations tix = ui for i = 1, 2, 3, ..... n, between hilbert spaces and give necessary and sucient conditions for the existence of common hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. also we study the moore-penrose inverse of a n*1 block operator matrix and then give the general form of common hermitian solutions to this system of equations. cosequently, we give the necessary and sucient conditions for the existence of common hermitian solutions to the system of operator equations tixvi = ui, for i = 1, 2, 3, .... n and also present the necessary conditions for solvability of the equation σ n i=1 tixi = u.
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کلیدواژه
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Operator equation; Hermitian solution; Common solution; Existence of solution; Moore Penrose inverse
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آدرس
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payame noor university, department of mathematics, Iran, amirkabir university of technology, department of mathematics and computer science, Iran, payame noor university, department of mathematics, Iran
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Authors
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