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Extremal Extensions of the Tensor Product of Nonnegative Operators
Author(s) -
Nafalska Maria Magdalena
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910299
Subject(s) - tensor product , mathematics , class (philosophy) , extension (predicate logic) , separable space , product (mathematics) , pure mathematics , hilbert space , von neumann architecture , tensor product of hilbert spaces , tensor (intrinsic definition) , algebra over a field , mathematical analysis , computer science , tensor contraction , geometry , artificial intelligence , programming language
For densely defined nonnegative operators A and B acting in separable Hilbert spaces we describe the Friedrichs and the Krein‐von Neumann extension of the tensor product $A \hat\otimes B$ . Moreover, we discuss the class of extremal extensions of $A \hat\otimes B$ . An application is presented as well. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)