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1.
Stephen J. Gardiner 《Proceedings of the American Mathematical Society》1996,124(4):1149-1157
Let , where is polar and compact and is a domain with Green function . We characterize those subsets of which have the following property: Every positive continuous function on can be written as , where and for each .
2.
Uri Fixman Frank Okoh G. K. R. Rao 《Proceedings of the American Mathematical Society》1996,124(4):1133-1138
Let be a complex Lebesgue space with a unique duality map from to , the conjugate space of . Let be a compact operator on . This paper focuses on properties of and . We adapt an example due to Halmos to show that for , there is a compact operator on with the semi-open interval . So is not attained as a maximum. A corollary of the main result in this paper is that if , and , then is attained as a maximum.
3.
Dusan Repovs Arkadij B. Skopenkov Evgenij V. Scepin 《Proceedings of the American Mathematical Society》1996,124(4):1219-1226
We give the characterization of -homogeneous compacta in : Let be a locally compact (possibly nonclosed) subset of . Then is -homogeneous if and only if is a -submanifold of .
4.
J. A. Erdos 《Proceedings of the American Mathematical Society》1996,124(4):1127-1131
Anoussis and Katsoulis have obtained a criterion for the space to have a closed complement in , where is a completely distributive commutative subspace lattice. They show that, for a given , the set of for which this complement exists forms an interval whose endpoints are harmonic conjugates. Also, they establish the existence of a lattice for which has no complement for any . However, they give no specific example. In this note an elementary demonstration of a simple example of this phenomenon is given. From this it follows that for a wide range of lattices , fails to have a complement for any .
5.
Alejandro Illanes 《Proceedings of the American Mathematical Society》1996,124(4):1243-1246
A topological space is -resolvable if has disjoint dense subsets. In this paper, we prove that if is -resolvable for each positive integer , then is -resolvable.
6.
A probability measure on a product space is said to be bistochastic with respect to measures on and on if the marginals and are exactly and . A solution is presented to a problem of Arveson about sets which are of measure zero for all such .
7.
Stephen Watson 《Proceedings of the American Mathematical Society》1996,124(4):1281-1284
Two topologies and on a fixed set are -complements if is the cofinite topology and is a sub-base for the discrete topology. In 1967, Steiner and Steiner showed that of any two -complements on a countable set, at least one is not Hausdorff. In 1969, Anderson and Stewart asked whether a Hausdorff topology on an uncountable set can have a Hausdorff -complement. We construct two homeomorphic completely regular -complementary topologies.
8.
Let and be real Banach spaces. A map between and is called an -bi-Lipschitz map if for all . In this note we show that if is an -bi-Lipschitz map with from onto , then is almost linear. We also show that if is a surjective -bi-Lipschitz map with , then there exists a linear isomorphism such that
where as and .
9.
To a given basis on an -dimensional Hilbert space , we associate the algebra of all linear operators on having every as an eigenvector. So, is commutative, semisimple, and -dimensional. Given two algebras of this type, and , there is a natural algebraic isomorphism of and . We study the question: When does preserve the operator norm?
10.
We prove that if a commutative semi-simple Banach algebra is the range of a ring homomorphism from a commutative -algebra, then is -equivalent, i.e. there are a commutative -algebra and a bicontinuous algebra isomorphism between and . In particular, it is shown that the group algebras , and the disc algebra are not ring homomorphic images of -algebras.
11.
Jon F. Carlson Hans-Werner Henn 《Proceedings of the American Mathematical Society》1996,124(3):665-670
Suppose that is a compact Lie group or a discrete group of finite virtual cohomological dimension and that is a field of characteristic . Suppose that is a set of elementary abelian -subgroups such that the cohomology is detected on the centralizers of the elements of . Assume also that is closed under conjugation and that is in whenever some subgroup of is in . Then there exists a regular element in the cohomology ring such that the restriction of to an elementary abelian -subgroup is not nilpotent if and only if is in . The converse of the result is a theorem of Lannes, Schwartz and the second author. The results have several implications for the depth and associated primes of the cohomology rings.
12.
Bangming Deng 《Proceedings of the American Mathematical Society》1996,124(6):1673-1677
Let be an artin algebra. This paper presents a sufficient condition for the subcategory of to be contravariantly finite in , where is the subcategory of consisting of --modules of projective dimension less than or equal to . As an application of this condition it is shown that is contravariantly finite in for each when is stably equivalent to a hereditary algebra.
13.
Michael Cwikel Mieczyslaw Mastylo 《Proceedings of the American Mathematical Society》1996,124(4):1103-1109
It is shown that the complex interpolation spaces and do not coincide with or and also that the couple is not a Calderón couple. Similar results are also obtained for the couples and when .
14.
Let be a locally compact group equipped with right Haar measure. The right differences of functions on are defined by for . Let and suppose for some and all . We prove that is a right uniformly continuous function of . If is abelian and the Beurling spectrum does not contain the unit of the dual group , then we show . These results have analogues for functions , where is a separable or reflexive Banach space. Finally, we apply our methods to vector-valued right uniformly continuous differences and to absolutely continuous elements of left Banach -modules.
15.
For a separable infinite-dimensional Hilbert space , we consider the full algebra of bounded linear transformations and the unique non-trivial norm-closed two-sided ideal of compact operators . We also consider the quotient -algebra with quotient map
For any -subalgebra of , the relative commutant is given by for all in . It was shown by D. Voiculescu that, for any separable unital -subalgebra of ,
In this note, we exhibit a non-separable unital -subalgebra of for which (VDCT) fails.
16.
Christian Friesen Doug Hensley 《Proceedings of the American Mathematical Society》1996,124(9):2661-2673
Given a finite field of order and polynomials of degrees respectively, there is the continued fraction representation . Let denote the number of such pairs for which and for . We give both an exact recurrence relation, and an asymptotic analysis, for . The polynomial associated with the recurrence relation turns out to be of P-V type. We also study the distribution of . Averaged over all and as above, this presents no difficulties. The average value of is , and there is full information about the distribution. When is fixed and only is allowed to vary, we show that this is still the average. Moreover, few pairs give a value of that differs from this average by more than
17.
Let be a Banach space. For we prove that the identity map is -summing if and only if the operator is nuclear for every unconditionally summable sequence in , where is the conjugate number for . Using this result we find a characterization of Banach spaces in which every -weakly summable sequence lies inside the range of an -valued measure (equivalently, every -weakly summable sequence in , satisfying that the operator is compact, lies in the range of an -valued measure) with bounded variation. They are those Banach spaces such that the identity operator is -summing.
18.
P. D. Johnson Jr. R. N. Mohapatra Jr. David Ross Jr. 《Proceedings of the American Mathematical Society》1996,124(2):543-547
Suppose is a non-increasing sequence of non-negative numbers with , , , and is the lower triangular matrix defined by , , and , . We show that the operator norm of as a linear operator on is no greater than , for ; this generalizes, yet again, Hardy's inequality for sequences, and simplifies and improves, in this special case, more generally applicable results of D. Borwein, Cass, and Kratz. When the tend to a positive limit, the operator norm of on is exactly . We also give some cases when the operator norm of on is less than .
19.
L. J. Bunce J. D. Maitland Wright 《Proceedings of the American Mathematical Society》1996,124(8):2377-2381
Let be a -algebra, and let be a (local) quasi-trace on . Then is linear if, and only if, the restriction of to the closed unit ball of is uniformly weakly continuous.
20.
On a polynomial inequality of Kolmogoroff's type 总被引:1,自引:0,他引:1
We prove an inequality of the form
for polynomials of degree and any fixed . Here is the -norm on with a weight . The coefficients and are given explicitly and depend on and only. The equality is attained for the Hermite orthogonal polynomials .