As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelope...As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H .展开更多
Suppose that U is a norm closed nest algebra module. Using the characterization of rank one operators in U⊥, a complete description of the extreme points of the unit ball U1 is given.
In this paper, the Ext groups of Hardy modules over the polydisk algebra A(Dn) are cal-culated. Of particular importance is that the calculating of Ext-groups is closely related toharmonic analysis of polydisks. Final...In this paper, the Ext groups of Hardy modules over the polydisk algebra A(Dn) are cal-culated. Of particular importance is that the calculating of Ext-groups is closely related toharmonic analysis of polydisks. Finally, the authors point out that Ext-groups reveal rigidityof Hardy submodules over A(Dn) for n > 1.展开更多
文摘As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H .
文摘Suppose that U is a norm closed nest algebra module. Using the characterization of rank one operators in U⊥, a complete description of the extreme points of the unit ball U1 is given.
文摘In this paper, the Ext groups of Hardy modules over the polydisk algebra A(Dn) are cal-culated. Of particular importance is that the calculating of Ext-groups is closely related toharmonic analysis of polydisks. Finally, the authors point out that Ext-groups reveal rigidityof Hardy submodules over A(Dn) for n > 1.
