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1.
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.
2.
Let be a regular local ring containing a field. We give a refinement of the Briançon-Skoda theorem showing that if is a minimal reduction of where is -primary, then where and is the largest ideal such that . The proof uses tight closure in characteristic and reduction to characteristic for rings containing the rationals.
3.
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.
4.
Jodie D. Novak 《Proceedings of the American Mathematical Society》1996,124(3):969-975
For the Lie group , let be the open orbit of Lagrangian planes of signature in the generalized flag variety of Lagrangian planes in . For a suitably chosen maximal compact subgroup of and a base point we have that the orbit of is a maximal compact subvariety of . We show that for the connected component containing in the space of translates of which lie in is biholomorphic to , where denotes with the opposite complex structure.
5.
Alexander Kumjian Iain Raeburn Dana P. Williams 《Proceedings of the American Mathematical Society》1996,124(3):809-817
If is a locally compact space which admits commuting free and proper actions of locally compact groups and , then the Brauer groups and are naturally isomorphic.
6.
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.
7.
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?
8.
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 .
9.
Let be a subgroup of , where is a Dedekind ring, and let be the -ideal generated by , where . The subgroup is called standard iff contains the normal subgroup of generated by the -elementary matrices. It is known that, when , is standard iff is normal in . It is also known that every standard subgroup of is normal in when is an arithmetic Dedekind domain with infinitely many units. The ring of integers of an imaginary quadratic number field, , is one example (of three) of such an arithmetic domain with finitely many units. In this paper it is proved that every Bianchi group has uncountably many non-normal, standard subgroups. This result is already known for related groups like .
10.
Mario Petrich C. M. Reis G. Thierrin 《Proceedings of the American Mathematical Society》1996,124(3):655-663
11.
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.
12.
Simba A. Mutangadura 《Proceedings of the American Mathematical Society》1996,124(3):907-918
We continue here the study begun in earlier papers on implementation of comparative probability by states. Let be a von Neumann algebra on a Hilbert space and let denote the projections of . A comparative probability (CP) on (or more correctly on is a preorder on satisfying:
- with for some .
- If , then either or .
- If , and are all in and , , then .
13.
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.
14.
Haruto Ohta 《Proceedings of the American Mathematical Society》1996,124(3):961-967
Answering a question of Eklof-Mekler (Almost free modules, set-theoretic methods, North-Holland, Amsterdam, 1990), we prove: (1) If there exists a non-reflecting stationary set of consisting of ordinals of cofinality for each , then there exist abelian groups such that and for each . (2) There exist abelian groups such that for each and for each . The groups are the groups of -valued continuous functions on a topological space and their dual groups.
15.
Ken'ichi Ohshika 《Proceedings of the American Mathematical Society》1996,124(3):739-743
Two Kleinian groups and are said to be topologically conjugate when there is a homeomorphism such that . It is conjectured that if two Kleinian groups and are topologically conjugate, one is a quasi-conformal deformation of the other. In this paper generalizing Minsky's result, we shall prove that this conjecture is true when is finitely generated and freely indecomposable, and the injectivity radii of all points of and are bounded below by a positive constant.
16.
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 .
17.
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 .
18.
Sam Huckaba 《Proceedings of the American Mathematical Society》1996,124(5):1393-1401
A -dimensional version is given of a -dimensional result due to C. Huneke. His result produced a formula relating the length to the difference , where is primary for the maximal ideal of a -dimensional Cohen-Macaulay local ring , is a minimal reduction of , , and is the Hilbert-Samuel polynomial of . We produce a formula that is valid for arbitrary dimension, and then use it to establish some formulas for the Hilbert coefficients of . We also include a characterization, in terms of the Hilbert coefficients of , of the condition .
19.
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.
20.
D. D. Anderson Bernadette Mullins 《Proceedings of the American Mathematical Society》1996,124(2):389-396
An integral domain is a finite factorization domain if each nonzero element of has only finitely many divisors, up to associates. We show that a Noetherian domain is an FFD for each overring of that is a finitely generated -module, is finite. For local this is also equivalent to each being finite. We show that a one-dimensional local domain is an FFD either is finite or is a DVR.