Displaying similar documents to “A characterization of formally symmetric unbounded operators.”

Generalized D-Symmetric Operators I

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.

A study of an operator arising in the theory of circular plates

Leopold Herrmann (1988)

Aplikace matematiky

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The operator L 0 : D L 0 ⊂ H → H , L 0 u = 1 r d d r r d d r 1 r d d r r d u d r , D L 0 = { u ∈ C 4 ( [ 0 , R ] ) , u ' ( 0 ) = u ' ' ' ' ( 0 ) = 0 , u ( R ) = u ' ( R ) = 0 } , H = L 2 , r ( 0 , R ) is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on L 0 (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 L 0 u = g and u t t + L 0 u = g , respectively.