-symmetric operators: comments and some open problems.
Mecheri, Salah (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Mecheri, Salah (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Kostenko, A.S. (2005)
Zapiski Nauchnykh Seminarov POMI
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Bouali, S., Ech-chad, M. (2008)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary: 47B47, 47B10; secondary 47A30. Let H be an infinite-dimensional complex Hilbert space and let A, B ∈ L(H), where L(H) is the algebra of operators on H into itself. Let δAB: L(H) → L(H) denote the generalized derivation δAB(X) = AX − XB. This note will initiate a study on the class of pairs (A,B) such that [‾(R(δAB))] = [‾(R(δB*A*))]; i.e. [‾(R(δAB))] is self-adjoint.
Mecheri, Salah (2009)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Hebbeche, A. (2005)
Journal of Applied Mathematics
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El-Sabbagh, A.A. (1997)
International Journal of Mathematics and Mathematical Sciences
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Leopold Herrmann (1988)
Aplikace matematiky
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The operator , , , is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types and , respectively.