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1.
Suppose that we are given a set of powers of a prime and that . A technique is presented that enables the construction of a -group of specified nilpotence class such that its set of irreducible character degrees is exactly . If , then this can be done for and if , then the only requirement is . 相似文献
2.
Let be a nest algebra and its invariant projection (or subspace) lattice. In this paper, using order homomorphisms of , we give necessary and sufficient conditions on bounded linear operators and on a Hilbert space to guarantee the existence of an operator in a certain -module such that . 相似文献
3.
Let be a -semigroup with generator on a Banach space . Let be a fixed element. We prove the following individual stability results. (i) Suppose is an ordered Banach space with weakly normal closed cone and assume there exists such that for all . If the local resolvent admits a bounded analytic extension to the right half-plane 0\}$">, then for all and we have
(ii) Suppose is a rearrangement invariant Banach function space over with order continuous norm. If is an element such that defines an element of , then for all and we have
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4.
Let be the algebra of all bounded operators on a Hilbert space . Let be a continuous function on the closed disk and let for some 0,$"> for all and all with . Then is differentiable on . The paper shows that the function may have a discontinuous derivative. 相似文献
5.
Let be either the hyperbolic space or the unit sphere , and let be the set of all -dimensional totally geodesic submanifolds of . For and , the totally geodesic Radon transform is studied. By averaging over all at a distance from , and applying Riemann-Liouville fractional differentiation in , S. Helgason has recovered . We show that in the hyperbolic case this method blows up if does not decrease sufficiently fast. The situation can be saved if one employs Marchaud's fractional derivatives instead of the Riemann-Liouville ones. New inversion formulas for , are obtained. 相似文献
6.
Let be the collection of lower triangular Toeplitz matrices and let be the collection of lower triangular Toeplitz contractions. We show that is compact and strictly convex, in the spectral norm, with respect to ; that is, is compact, convex and , where and denote the topological boundary with respect to and the set of extreme points, respectively. As an application, we show that the reduced Cowen set for an analytic polynomial is strictly convex; more precisely, if is an analytic polynomial and if , then is strictly convex. This answers a question of C. Cowen for the case of analytic polynomials. 相似文献
7.
Let be a compact space and let , be a (real, for simplicity) Banach space. We consider the space of all continuous -valued functions on , with the supremum norm . We prove in this paper a Bochner integral representation theorem for bounded linear operators
which satisfy the following condition: where is the conjugate space of . In the particular case where , this condition is obviously satisfied by every bounded linear operator and the result reduces to the classical Riesz representation theorem. If the dimension of is greater than , we show by a simple example that not every bounded linear admits an integral representation of the type above, proving that the situation is different from the one dimensional case. Finally we compare our result to another representation theorem where the integration process is performed with respect to an operator valued measure. 相似文献
8.
We study the operator equation , where the operators and are given and the operator is required to lie in some von Neumann algebra. We derive a necessary and sufficient condition for the existence of a solution . The condition is that there must exist a constant so that, for all finite collections of operators in the commutant, and all collections of vectors , we have We also study the equality , in connection with solving the equation where the operator is required to lie in some CSL algebra. 相似文献
9.
Let be Banach spaces and let be closed operator ideals. Let be a Banach space having the Radon-Nikodým property. The main results are as follows. If is a Hahn-Banach extension operator, then there exists a set of Hahn-Banach extension operators , , such that , where . If is an ideal in for all equivalently renormed versions of , then there exist Hahn-Banach extension operators and such that . 相似文献
10.
Let be a Hilbert -module over the -algebra of all compact operators on a Hilbert space. It is proved that any function which preserves the absolute value of the -valued inner product is of the form , where is a phase function and is an -linear isometry. The result generalizes Molnár's extension of Wigner's classical unitary-antiunitary theorem. 相似文献
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