共查询到20条相似文献,搜索用时 15 毫秒
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George A. Elliott Katsunori Kawamura 《Transactions of the American Mathematical Society》2008,360(9):4841-4862
The category of Hilbert C*-modules over a given C*-algebra is shown to be equivalent to a certain simply described category of Hilbert bundles (i.e., continuous fields of Hilbert spaces) over the space of pure states of the C*-algebra with the zero functional adjoined.
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The aim of the present paper is to solve some major open problems of Hilbert C*-module theory by applying various aspects of multiplier C*-theory. The key result is the equivalence established between positive invertible quasi-multipliers of the C*-algebra of compact operators on a Hilbert C*-module {, ., } and A-valued inner products on , inducing an equivalent norm to the given one. The problem of unitary isomorphism of C*-valued inner products on a Hilbert C*-module is considered and new criteria are formulated. Countably generated Hilbert C*-modules turn out to be unitarily isomorphic if they are isomorphic as Banach C*-modules. The property of bounded module operators on Hilbert C*-modules of being compact and/or adjointable is unambiguously connected to operators with respect to any choice of the C*-valued inner product on a fixed Hilbert C*-module if every bounded module operator possesses an adjoint operator on the module. Every bounded module operator on a given full Hilbert C*-module turns out to be adjointable if the Hilbert C*-module is orthogonally complementary. Moreover, if the unit ball of the Hilbert C*-module is complete with respect to a certain locally convex topology, then these two properties are shown to be equivalent to self-duality. 相似文献
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Adrian R. Wadsworth 《代数通讯》2013,41(8):863-872
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Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombieri and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C *-modules. 相似文献
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张伦传 《应用泛函分析学报》2003,5(3):210-212
获得了Hilbert C^*-模之间的两个同构定理.作为推论,证明了C^*-代数上每个可数生成的Hilbert C^*-模均稳定酉等价于A。 相似文献
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We present a new operator equality in the framework of Hilbert C*-modules. As a consequence, we get an extension of the Euler–Lagrange type identity in the setting of Hilbert bundles as well as several generalized operator Bohr's inequalities due to O. Hirzallah, W.-S. Cheung, J.E. Pe?ari? and F. Zhang. 相似文献
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观察到Hilbert C*-模中融合框架原定义的不合理性,然后通过权重集的选取将其改进,得到融合框架的新定义并给出其等价形式.特别地,利用算子理论方法得到了Hilbert C*-模中融合框架的一个新刻画. 相似文献
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V. M. Futorny 《Ukrainian Mathematical Journal》1991,43(2):250-254
Generalized Verma modules over the Lie algebra sl(3, ) that contain no highest vector are studied. Such modules are generated by semiprimitive elements. The composition structure of these modules is studied, an irreducibility criterion is given. Explicit formulas for semiprimitive elements are obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 2, pp. 281–285, February, 1991. 相似文献
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Summary The authors' approach to Gersten's graphical model of an automorphism is generalized to prove the theorem of the title, resolving a conjecture of Stallings. 相似文献
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Mitsuyasu Hashimoto 《Proceedings of the American Mathematical Society》2005,133(8):2233-2235
We prove the following. Let be a Noetherian commutative ring, a finitely generated -algebra, and a pure -subalgebra of . Then is finitely generated over .
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Seán Dineen 《Mathematische Annalen》1972,196(2):106-116
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