摘要:

AbstractBehavior of weak measures of noncompactness under real interpolation is investigated. It is shown that “convexity type” theorems hold true for weak measures of noncompactn

ISSN:0025-584X    

DOI:10.1002/mana.19951750102

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractSummary. This paper develops renewal theory for a rather general class of random walksSNincluding linear submartingales with positive drift. The basic assumption onSNis that their conditional increment distribution functions with respect to some filtration ℱℕare bounded from above and below by integrable distribution functions. Under a further mean stability condition these random walks turn out to be natural candidates for satisfying Blackwell‐type renewal theorems. In a companion paper [2], certain uniform lower and upper drift bounds forSN, describing its average growth on finite remote time intervals, have been introduced and shown to be equal in case the afore‐mentioned mean stability condition holds true. With the help of these bounds we give lower and upper estimates forH*U(B), whereUdenotes the renewal measure ofSN,Ha suitable delay distribution andBa Borel subset of IR. This is then further utilized in combination with a coupling argument to prove the principal result, namely an extension of Blackwell's renewal theorem to random walks of the previous type whose conditional increment distribution additionally contain a subsequence with a common component in a certain sense. A number of examples are also pr

ISSN:0025-584X    

DOI:10.1002/mana.19951750103

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractLetAbe a normal operator in ℬ︁(H), H a complex Hilbert space, and let ℛA= ≷ {AX‐XA:X ∈ ℬ︁(H)} be the commutator subspace of ℬ︁(H) associated withA. IfBin ℬ︁(H) commutes withA, thenBis orthogonal to ℛAwith respect to the spectral norm; i.e., the null operator is an element of best approximation ofBin ℛA. This was proved byJ. Andersonin 1973 and extended byP. J. Maherwith respect to the Schattenp‐norm recently.We take a look at their result from a more approximation theoretical point of view in the finite dimensional setting; in particular, we characterize all elements of best approximation ofBinRAand prove that the metric proje

ISSN:0025-584X    

DOI:10.1002/mana.19951750104

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractIn this paper a method is developed to calculate the Floquet exponents of the matrix‐valued version of Hill's equation using infinite determinants. It is shown that the Floquet exponents are precisely the zeros of an infinite determinant corresponding to the differential equation. The proof of this result uses the continuity and holomorphy of the infinite determinan

ISSN:0025-584X    

DOI:10.1002/mana.19951750105

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractThe aim of the present paper is to describe self‐duality andC*‐reflexivity of Hilbert A‐modules ℳ︁ over monotone completeC*‐algebras A by the completeness of the unit ball of ℳ︁ with respect to two types of convergence being defined, and by a structural criterion. The derived results generalize earlier results ofH. Widom[Duke Math. J. 23, 309‐324, MR 17 # 1228] andW. L. Paschke[Trans. Amer. Mat. Soc.182, 443‐468, MR 50 # 8087, Canadian J. Math. 26, 1272‐1280, MR 57 # 10433]. For HilbertC*‐modules over commutativeAW*‐algebras the equivalence of the self‐duality property and of the Kaplansky‐Hilbert property is reproved, (cf.M. Ozawa[J. Math. Soc. Japan 36, 589‐609, MR 85 # 46068]). Especially, one derives that for aC*‐algebra A the A‐valued inner product of every Hilbert A‐module ℳ︁ can be continued to an A‐valued inner product on it's A‐dual Banach A‐module ℳ︁' turning ℳ︁' to a self‐dual Hilbert A‐module if and only if A is monotone complete (or, equivalently, additively complete) generalizing a result ofM. Hamana[Internat. J. Math. 3 (1992), 185 ‐ 204]. A classification of countably generated self‐dual Hilbert A‐modules over monotone completeC*‐algebras A is established. The set of all bounded module operatorsEnd′(ℳ︁) on self‐dual Hilbert A‐modules ℳ︁ over monotone completeC*‐algebras A is proved again to be a m

ISSN:0025-584X    

DOI:10.1002/mana.19951750106

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractIt is shown that para‐multiplication applies to a certain product π(u, v) defined for appropriateuandvin

ISSN:0025-584X    

DOI:10.1002/mana.19951750107

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractTwo different inverse function theorems, one of Nash‐Moser type, the other due toH. Omori, are extended to obtain special surjectivity results in locally convex and locally pseudo‐convex Fréchet algebras generated by group actions and derivations. In particular, the following factorization problem is discussed. Let Ψ be a locally pseudo‐convex Fréchet algebra with uniteand T+: Ψ → Ψ a continuous linear operator. Does there exist a neighborhoodUof 0 such that the equation\documentclass{article}\pagestyle{empty}\begin{document}$e - y = (e - t_ + x)(e - t_ - x)$\end{document}where T‐=IΨ‐ T, has a solutionx

ISSN:0025-584X    

DOI:10.1002/mana.19951750108

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractThe authors study the partial fraction decomposition of narrow class partial zeta functions of real quadratic number fields at nonpositive integer arguments and obtain an analogue of the classical v. Staudt/Clausen Theorem. The main results follow from the study of the residues ofp‐adic zeta functions associated with ray classes of modulus (p) for all rational primes

ISSN:0025-584X    

DOI:10.1002/mana.19951750109

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractEs wird eine asymptotische Formel angegeben für den konformen Modul eines Vierecks mit zwei Gegenseiten, die Parallelkurven kleinen Abstand sind

ISSN:0025-584X    

DOI:10.1002/mana.19951750110

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractSmooth complex algebraic surfacesS ⊆Pnof degreedand class ℳ︁ satisfyingd

ISSN:0025-584X    

DOI:10.1002/mana.19951750111

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY