共查询到20条相似文献,搜索用时 31 毫秒
1.
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.
2.
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 .
3.
Ricardo Estrada 《Proceedings of the American Mathematical Society》1996,124(4):1205-1212
Let be a periodic distribution of period . Let be its Fourier series. We show that the distributional point value exists and equals if and only if the partial sums converge to in the Cesàro sense as for each .
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.
Let denote the rational curve with nodes obtained from the Riemann sphere by identifying 0 with and with for , where is a primitive th root of unity. We show that if is even, then has no smooth Weierstrass points, while if is odd, then has smooth Weierstrass points.
6.
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.
7.
Consider the curve , where is absolutely continuous on . Then has finite length, and if is the -neighborhood of in the uniform norm, we compare the length of the shortest path in with the length of . Our main result establishes necessary and sufficient conditions on such that the difference of these quantities is of order as . We also include a result for surfaces.
8.
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 .
9.
Ludomir Newelski 《Proceedings of the American Mathematical Society》1996,124(8):2519-2525
Assume is superstable, is a formula over , is countable and is countable and . We investigate models in assuming has the prime model property. We prove some corollaries on the number of models in . We show an example of an -stable and with having exactly 3 models.
10.
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 .
11.
E. Prestini 《Proceedings of the American Mathematical Society》1996,124(4):1171-1175
We study the operators
where is the Hardy-Littlewood maximal function, the Hilbert transform or Carleson operator.
Under suitable conditions on the weight of exponential type, we prove boundedness of from spaces, defined on with respect to the measure to with the same density measure. These operators, that arise in questions of harmonic analysis on noncompact symmetric spaces, are bounded from to if and only if .
12.
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?
13.
Jacques Delaporte Antoine Derighetti 《Proceedings of the American Mathematical Society》1996,124(4):1159-1169
We compute the best bound for the approximate units of the augmentation ideal of the group algebra of a locally compact amenable group . More generally such a calculation is performed for the kernel of the canonical map from onto , being a closed amenable subgroup of . Analogous results involving certain ideals of the Fourier algebra of an amenable group are also discussed.
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.
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 .
16.
It is proved that if are bounded -semigroups on Banach spaces and , resp., and , are bounded operators with dense ranges such that intertwines with and commutes with , then is strongly stable provided ---the generator of ---does not have eigenvalue on . An analogous result holds for power-bounded operators.
17.
Dong-Kwan Shin 《Proceedings of the American Mathematical Society》1996,124(12):3641-3646
Let be a smooth minimal threefold of general type and let be an integer . Assume that the image of the pluricanonical map of is a curve. Then a simple computation shows that is necessarily or . When with a numerical condition or when , we obtain two inequalities and , where is the irregularity of and is the Euler characteristic of .
18.
Young-One Kim 《Proceedings of the American Mathematical Society》1996,124(3):819-830
Let be a nonconstant real entire function of genus and assume that all the zeros of are distributed in some infinite strip , . It is shown that (1) if has nonreal zeros in the region , and has nonreal zeros in the same region, and if the points and are located outside the Jensen disks of , then has exactly critical zeros in the closed interval , (2) if is at most of order , , and minimal type, then for each positive constant there is a positive integer such that for all has only real zeros in the region , and (3) if is of order less than , then has just as many critical points as couples of nonreal zeros.
19.
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.
20.
Xiangrong Yin Benjamin Muckenhoupt 《Proceedings of the American Mathematical Society》1996,124(1):75-81
For nonnegative Borel measures on and for the maximal geometric mean operator , we characterize the weight pairs for which is of weak type and of strong type , . No doubling conditions are needed. We also note that a previously published different characterization for the strong type inequality for has an incorrect proof.