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- Hilbert–Schmidt_operator abstract "In mathematics, a Hilbert–Schmidt operator, named for David Hilbert and Erhard Schmidt, is a bounded operator A on a Hilbert space H with finite Hilbert–Schmidt normwhere is the norm of H and an orthonormal basis of H for an index set . Note that the index set need not be countable. This definition is independent of the choice of the basis, and thereforefor and the Schatten norm of . In Euclidean space is also called Frobenius norm, named for Ferdinand Georg Frobenius.The product of two Hilbert–Schmidt operators has finite trace class norm; therefore, if A and B are two Hilbert–Schmidt operators, the Hilbert–Schmidt inner product can be defined asThe Hilbert–Schmidt operators form a two-sided *-ideal in the Banach algebra of bounded operators on H. They also form a Hilbert space, which can be shown to be naturally isometrically isomorphic to the tensor product of Hilbert spaceswhere H* is the dual space of H.The set of Hilbert–Schmidt operators is closed in the norm topology if, and only if, H is finite-dimensional.An important class of examples is provided by Hilbert–Schmidt integral operators.Hilbert–Schmidt operators are nuclear operators of order 2, and are therefore compact.".
- Hilbert–Schmidt_operator wikiPageID "976673".
- Hilbert–Schmidt_operator wikiPageRevisionID "599174049".
- Hilbert–Schmidt_operator subject Category:Operator_theory.
- Hilbert–Schmidt_operator comment "In mathematics, a Hilbert–Schmidt operator, named for David Hilbert and Erhard Schmidt, is a bounded operator A on a Hilbert space H with finite Hilbert–Schmidt normwhere is the norm of H and an orthonormal basis of H for an index set . Note that the index set need not be countable. This definition is independent of the choice of the basis, and thereforefor and the Schatten norm of .".
- Hilbert–Schmidt_operator label "Hilbert-Schmidt-Operator".
- Hilbert–Schmidt_operator label "Hilbert–Schmidt operator".
- Hilbert–Schmidt_operator label "Operator Hilberta-Schmidta".
- Hilbert–Schmidt_operator label "Operatore di Hilbert-Schmidt".
- Hilbert–Schmidt_operator label "Оператор Гильберта — Шмидта".
- Hilbert–Schmidt_operator label "ヒルベルト＝シュミット作用素".
- Hilbert–Schmidt_operator sameAs Hilbert%E2%80%93Schmidt_operator.
- Hilbert–Schmidt_operator sameAs Hilbert-Schmidt-Operator.
- Hilbert–Schmidt_operator sameAs Operatore_di_Hilbert-Schmidt.
- Hilbert–Schmidt_operator sameAs ヒルベルト＝シュミット作用素.
- Hilbert–Schmidt_operator sameAs Operator_Hilberta-Schmidta.
- Hilbert–Schmidt_operator sameAs Q1518047.
- Hilbert–Schmidt_operator sameAs Q1518047.
- Hilbert–Schmidt_operator wasDerivedFrom Hilbert–Schmidt_operator?oldid=599174049.