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In this paper, we study the commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonic Bergman space. 相似文献
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For type factors with , we show that the sets and are finite. Moreover, , the set of intermediate subfactors, is finite if and only if it is equal to . If is an irreducible subfactor, then we recover a result of Y. Watatani.
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LI Weihua Institute of Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2005,48(9):1284-1295
Some basic questions on ultraproducts of C~*-algebras and von Neumann al- gebras,including the relation to K-theory of C~*-algebras are considered.More specifically, we prove that under certain conditions,the K-groups of ultraproduct of C~*-algebras are iso- morphic to the ultraproduct of respective K-groups of C~*-algebras.We also show that the ultraproducts of factors of type Ⅱ_1 are prime,i.e.not isomorphic to any non-trivial tensor product. 相似文献
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Pengtong Li Shijie Lu Jipu Ma 《Proceedings of the American Mathematical Society》2004,132(7):2005-2012
Let be a subspace lattice on a normed space containing a nontrivial comparable element. If commutes with all the operators in , then there exists a scalar such that . Furthermore, we classify the class of completely distributive subspace lattices into subclasses called Type , Type and Type , respectively. It is shown that nontrivial nests or, more generally, completely distributive subspace lattices with a comparable element are Type , and that nontrivial atomic Boolean subspace lattices are Type .
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