The classification of von Neumann algebras requires a good understanding of their orthogonal projections. We show that they form a complete lattice under the usual order given by positivity, so the supremum and infinum of any family of them belong to the von Neumann algebra W . We say two ...
摘要: WeconsiderrealAW*-algebras,thatis,KaplanskyalgebrasoverthefieldofrealnumbersAsinthecaseofcomplexvonNeumannalgebrasandcomplexAW*-algebras,realAW*-algebrasareclassifiedintermsoftypesofa?realAW*-alg关键词: and<IMGALIGN=ABSMIDDLEALT=$mathrm{III}$SRC=http://ejioporg/images/1064-5632/68/5/A01/tex...
We will see that the von Neumann algebras of type I behave most naturally from the classical point of view. The structure of such an algebra will be completely determined in terms of the spectrum of the center and a set of cardinal numbers. At this point, it should be mentioned that the...
Dragoş Ştefan, The set of types of n-dimensional semisimple and cosemisimple Hopf algebras is finite, J. Algebra 193 (1997), no. 2, 571-580, DOI 10.1006/jabr.1996.6991. MR1458803D. Stefan, The set of types of n-dimensional semisimple and cosemisimple Hopf algebras is finite, J. ...
STO~E~, E., Types of von Neumann algebras associated with extremal invariant states. Comm. Math. Phys., 6 (1967), 194-204.Stormer, Erling (1967), "Types of von Neumann Algebras Associated with Extremal In- variant States", Communications in Mathematical Physics 6: 194-204....
Criteria for the existence of the different types of conditional expectation and of the extension of the Lüders—von Neumann measurement are presented, and the question whether they coincide is studied. All this is done in the general framework of Jordan operator algebras. The examples considered ...
We investigate and characterize several kinds of elements such as units, idempotents, von Neumann regular, \\pi \\pi -regular and clean elements for skew PBW extensions over weak compatible rings. We also study the notions of Gelfand and Harmonic rings for these families of algebras. The ...