The curvature of a Hilbert module over C[z1, ... , zd]
نویسندگان
چکیده
منابع مشابه
The curvature of a Hilbert module over.
A notion of curvature is introduced in multivariable operator theory. The curvature invariant of a Hilbert module over C[z(1),., z(d)] is a nonnegative real number which has significant extremal properties, which tends to be an integer, and which is hard to compute directly. It is shown that for graded Hilbert modules, the curvature agrees with the Euler characteristic of a certain finitely gen...
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A notion of curvature is introduced in multivariable operator theory, that is, for commuting d tuples of operators acting on a common Hilbert space whose “rank” is finite in an appropriate sense. The curvature invariant is a real number in the interval [0, r] where r is the rank, and for good reason it is desireable to know its value. For example, there are significant and concrete consequences...
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A notion of curvature is introduced in multivariable operator theory and an analogue of the Gauss-Bonnet-Chern theorem is established. Applications are given to the metric structure of graded ideals in C[z1, . . . , zd], and the existence of “inner” sequences for closed submodules of the free Hilbert module H(C).
متن کاملResults on Hilbert coefficients of a Cohen-Macaulay module
Let $(R,m)$ be a commutative Noetherian local ring, $M$ a finitely generated $R$-module of dimension $d$, and let $I$ be an ideal of definition for $M$. In this paper, we extend cite[Corollary 10(4)]{P} and also we show that if $M$ is a Cohen-Macaulay $R$-module and $d=2$, then $lambda(frac{widetilde{I^nM}}{Jwidetilde{I^{n-1}M}})$ does not depend on $J$ for all $ngeq 1$, where $J$ is a minimal ...
متن کاملThe solutions to some operator equations in Hilbert $C^*$-module
In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1999
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.96.20.11096