Partial integral operators of Fredholm type on Kaplansky-Hilbert module over L0

Автор: Eshkabilov Yusup Kh., Kucharov Ramziddin R.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 3 т.23, 2021 года.

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The article studies some characteristic properties of self-adjoint partially integral operators of Fredholm type in the Kaplansky--Hilbert module L0[L2(Ω1)] over L0(Ω2). Some mathematical tools from the theory of Kaplansky--Hilbert module are used. In the Kaplansky--Hilbert module L0[L2(Ω1)] over L0(Ω2) we consider the partially integral operator of Fredholm type T1 (Ω1 and Ω2 are closed bounded sets in Rν1 and Rν2, ν1,ν2∈N, respectively). The existence of L0(Ω2) nonzero eigenvalues for any self-adjoint partially integral operator T1 is proved; moreover, it is shown that T1 has finite and countable number of real L0(Ω2)-eigenvalues. In the latter case, the sequence L0(Ω2)-eigenvalues is order convergent to the zero function. It is also established that the operator T1 admits an expansion into a series of ∇1-one-dimensional operators.

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Partial integral operator, kaplansky-hilbert module, l0-eigenvalue

Короткий адрес: https://sciup.org/143177811

IDR: 143177811   |   DOI: 10.46698/w5172-0182-0041-c

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