共查询到20条相似文献,搜索用时 15 毫秒
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Tensor productsZ=T
1⊗T
2 and multiplicationsZ=L
T
1
R
T
2 do not inherit Weyl’s theorem from Weyl’s theorem forT
1 andT
2. Also, Weyl’s theorem does not transfer fromZ toZ*. We prove that ifT
i,i=1, 2, has SVEP (=the single-valued extension property) at points in the complement of the Weyl spectrumσ
w(Ti) ofT
i, and if the operatorsT
i are Kato type at the isolated points ofσ(Ti), thenZ andZ* satisfy Weyl’s theorem. 相似文献
4.
Sheng-Ming Ma 《数学学报(英文版)》2009,25(11):1865-1874
This paper proves a theorem on the decay rate of the oscillatory integral operator with a degenerate C^∞ phase function, thus improving a classical theorem of HSrmander. The proof invokes two new methods to resolve the singularity of such kind of operators: a delicate method to decompose the operator and balance the L^2 norm estimates; and a method for resolution of singularity of the convolution type. The operator is decomposed into four major pieces instead of infinite dyadic pieces, which reveals that Cotlar's Lemma is not essential for the L^2 estimate of the operator. In the end the conclusion is further improved from the degenerate C^∞ phase function to the degenerate C^4 phase function. 相似文献
5.
Dug Hun Hong 《Fuzzy Optimization and Decision Making》2014,13(2):197-210
Recently, Zhao et al. (Euro J Oper Res 169:189–201, 2006) discussed a random fuzzy renewal process based on the random fuzzy theory and established Blackwell’s theorem in random fuzzy sense. They obtained Blackwell’s theorem for fuzzy variables by degenerating the process. However, this result is invalid. We provide some counterexamples and offer a corrected version of fuzzy Blackwell’s theorem. 相似文献
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A version of Engel’s theorem for Malcev superalgebras is proved in the spirit of theJacobson-Engel theorem for Lie algebras. Some consequences for the structure of Malcev superalgebras with trivial Lie nucleus are derived. 相似文献
7.
We prove that Menger’s theorem is valid for infinite graphs, in the following strong version: let A and B be two sets of vertices in a possibly infinite digraph. Then there exist a set of disjoint A–B paths, and a set S of vertices separating A from B, such that S consists of a choice of precisely one vertex from each path in . This settles an old conjecture of Erdős. 相似文献
8.
We prove a Siegel type statement for finitely generated -submodules of under the action of a Drinfeld module . This provides a positive answer to a question we asked in a previous paper. We also prove an analog for Drinfeld modules
of a theorem of Silverman for nonconstant rational maps of over a number field. 相似文献
9.
Tamás Titkos 《Positivity》2012,16(4):619-626
In this paper, we present a generalization of Ando??s theorem for nonnegative forms. He proved that the infimum of two positive operators A and B exists in the positive cone if and only if the generalized shorts [B]A and [A]B are comparable (see Ando et?al. in Problem of infimum in the positive cone, analytic and geometric inequalities and applications, Math. Appl. 478, pp 1?C12, 1999). That is, [A]B??? [B]A or [B]A??? [A]B. Using the concept of the parallel sum of nonnegative forms, Hassi, Sebestyén and de Snoo investigated the decomposability of a nonnegative form ${\mathfrak{t}}$ into an almost dominated and a singular part with respect to a nonnegative form ${\mathfrak{w}}$ (see Hassi et?al. in J. Funct. Anal. 257(12), 3858?C3894, 2009). Applying their results, we formulate a necessary and sufficient condition for the existence of the infimum of two nonnegative forms. 相似文献
10.
Let T be an algebraically paranormal operator acting on Hilbert
space. We prove : (i) Weyls theorem holds for f(T) for every f $\in$ H((T));
(ii) a-Browders theorem holds for f(S) for every S $\prec$ T and f $\in$ H((S));
(iii) the spectral mapping theorem holds for the Weyl spectrum of T and for
the essential approximate point spectrum of T. 相似文献
11.
Tord Sj?din 《manuscripta mathematica》2008,127(3):369-380
A theorem of Beurling states that if f satisfies , n = 1, 2,..., for some 0 < ρ < 2, on a real interval I, then f is analytic in a rhombus containing I. We study the corresponding problem for the quantum differences Δ
n
f (q, x), q > 1, n = 1, 2,..., for functions defined on (0, ∞) and prove quantitative and qualitative analogues of Beurling’s result. We also
characterize the analyticity of f on subintervals of (0, ∞) in q-analytic terms. 相似文献
12.
Fatemeh Zareh-Khoshchehreh 《代数通讯》2018,46(5):2171-2178
Let R be an associative ring with identity. For a given class 𝒮 of finitely presented left (respectively right) R-modules containing R, we present a complete characterization of 𝒮-pure injective modules and 𝒮-pure flat modules. Consider that 𝒮 is a class of (R,R)-bimodules containing R with the following property: every element of 𝒮 is a finitely presented left and right R-module. We give a necessary and sufficient condition for 𝒮 to have Lazard’s theorem, and then we present our desired Lazard’s theorem. 相似文献
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Daniel Zelinsky 《Israel Journal of Mathematics》1964,2(3):205-209
We give a new proof of the theorem that Amitsur’s complex for purely inseparable field extensions has vanishing homology in
dimensions higher than 2. This is accomplished by computing the kernel and cokernel of the logarithmic derivativet →Dt/t mapping the multiplicative Amitsur complex to the acyclic additive one (D is a derivation of the extension field).
This research was supported by National Science Foundation grant NSF GP 1649. 相似文献
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We prove an analogue of Sadullaev’s theorem concerning the size of the set where a maximal totally real manifold M can meet a pluripolar set. M has to be of class C 1 only. This readily leads to a version of Shcherbina’s theorem for C 1 functions f that are defined in a neighborhood of certain compact sets ${K\subset\mathbb{C}}We prove an analogue of Sadullaev’s theorem concerning the size of the set where a maximal totally real manifold M can meet a pluripolar set. M has to be of class C
1 only. This readily leads to a version of Shcherbina’s theorem for C
1 functions f that are defined in a neighborhood of certain compact sets
K ì \mathbbC{K\subset\mathbb{C}}. If the graph Γ
f
(K) is pluripolar, then
\frac?f?[`(z)]=0{\frac{\partial f}{\partial\bar z}=0} in the closure of the fine interior of K. 相似文献
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We prove the following theorem: For a partially ordered set Q such that every countable subset of Q has a strict upper bound, there is a forcing notion satisfying the countable chain condition such that, in the forcing extension, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechlers classical result in the theory of forcing. The corresponding theorem for the meager ideal was established by Bartoszyski and Kada.Research supported by NSERC. The first author thanks F.D. Tall and the Department of Mathematics at the University of Toronto for their hospitality during the academic year 2003/2004 when the present paper was completed.The second author was supported by Grant-in-Aid for Young Scientists (B) 14740058, MEXT.Mathematics Subject Classification (2000): 03E35, 03E17Revised version: 16 February 2004 相似文献
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In this work, we will prove the Dugundji extension theorem for the cone metric space. It is heavily reliant on the paracompactness of the cone topology that is proved by Ayse Sönmez in the paper Sönmez (2010) [11]. 相似文献
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Let H be a complex separable infinite dimensional Hilbert space. In this paper, a variant of the Weyl spectrum is discussed. Using the new spectrum, we characterize the necessary and sufficient conditions for both T and f(T) satisfying Weyl's theorem, where f ∈ Hol(σ(T)) and Hol(σ(T)) is defined by the set of all functions f which are analytic on a neighbourhood of σ(T) and are not constant on any component of σ(T). Also we consider the perturbations of Weyl's theorem for f(T). 相似文献
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If T or T* is an algebraically quasi-class A operator acting on an infinite dimensional separable Hilbert space then we prove that
Weyl’s theorem holds for f(T) for every f ∈ H(σ(T)), where H(σ(T)) denotes the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T* is algebraically quasi-class A then a-Weyl’s theorem holds for f(T). Also, if T or T* is an algebraically quasi-class A operator then we establish that the spectral mapping theorems for the Weyl spectrum and
the essential approximate point spectrum of T for every f ∈ H(σ(T)), respectively.
This research was supported by the Kyung Hee University Research Fund in 2007 (KHU- 20071605). 相似文献