共查询到20条相似文献,搜索用时 203 毫秒
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设H是一个希尔伯特空间,B(H)表示H上有界线性算子全体构成的集合.P,Q∈B(H)是两个正交射影.运用算子分块技巧给出了||PX-XQ||的一个刻画,在此基础上证明了不等式||P-Q||≤1.进一步运用算子分块技巧与算子谱理论,给出||P-Q||=1以及严格不等式成立的充分条件.最后给出P-Q可逆的一个等价刻画. 相似文献
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该文研究Hilbert空间H上正则射影对(P,Q)的性质和结构,给出H上有界线性算子A表示为两个正交射影乘积的充分必要条件. 相似文献
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对广义凸损失函数和变高斯核情形下正则化学习算法的泛化性能展开研究.其目标是给出学习算法泛化误差的一个较为满意上界.泛化误差可以利用正则误差和样本误差来测定.基于高斯核的特性,通过构构建一个径向基函数(简记为RBF)神经网络,给出了正则误差的上界估计,通过投影算子和再生高斯核希尔伯特空间的覆盖数给出样本误差的上界估计.所获结果表明,通过适当选取参数σ和λ,可以提高学习算法的泛化性能. 相似文献
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本文探讨加权Bergman空间Ap(φ)上Toeplitz算子,刻画了L∞(D)的使得符号在其中的Toeplitz算子的半换位子是紧算子的最大的自伴子代数Q,并计算了符号在Q中的Toeplitz算子的本质谱和Fredholm指标. 相似文献
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金蒙伟 《数学年刊B辑(英文版)》1993,(6)
设 T,S 为 R(K)循环的次正常算子,R(K)为 Dirichlet 代数.T 的极小正常扩张 mne(T)的谱σ(mneT)K.T 与 S 为拟相似.本文完全刻画了 T 的不变子空间.此外引进了超不变算子,并且给出了S|M 为超不变算子的充要条件. 相似文献
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有界线性算子的点谱和剩余谱分别可进-步细分为两类:σ_(p1),σ_(p2)和σ_(r1),σ_(r2).设H,K为无穷维可分的Hilbert空间,本文将对于给定的A ∈B (H),B ∈B(K),给出了缺项算子M_C=(AC/OB)关于分类后所得四种谱的扰动结果. 相似文献
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Alexander Pushnitski 《Journal of Functional Analysis》2011,261(7):2053-2081
Let H0 and H be self-adjoint operators in a Hilbert space. We consider the spectral projections of H0 and H corresponding to a semi-infinite interval of the real line. We discuss the index of this pair of spectral projections and prove an identity which extends the Birman-Schwinger principle onto the essential spectrum. We also relate this index to the spectrum of the scattering matrix for the pair H0, H. 相似文献
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An ordered pair (e,f) of idempotents of a regular semigroup is called a skew pair if ef is not idempotent whereas fe is idempotent.
Previously [1] we have established that there are four distinct types of skew pairs of idempotents. We have also described
(as quotient semigroups of certain regular Rees matrix semigroups [2]) the structure of the smallest regular semigroups that
contain precisely one skew pair of each of the four types, there being to within isomorphism ten such semigroups. These we
call the derived Rees matrix semigroups. In the particular case of full transformation semigroups we proved in [3] that TX contains all four skew pairs of idempotents if and only if |X| ≥ 6. Here we prove that TX contains all ten derived Rees matrix semigroups if and only if |X| ≥ 7. 相似文献
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John R. Swallow 《代数通讯》2013,41(12):3787-3796
We employ the recent results of Mestre [C. R. Acad. Sei. Paris, t. 319, Série I, pp. 781-782] to exhibit polynomials over Q(t) with the property that their splitting fields are regular, have Galois group PSL(2,7), and are embeddable in fields with Galois group SL(2,7) over Q(t). 相似文献
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In the smooth scattering theory framework, we consider a pair of self-adjoint operators H0, H and discuss the spectral projections of these operators corresponding to the interval (−∞,λ). The purpose of the paper is to study the spectral properties of the difference D(λ) of these spectral projections. We completely describe the absolutely continuous spectrum of the operator D(λ) in terms of the eigenvalues of the scattering matrix S(λ) for the operators H0 and H. We also prove that the singular continuous spectrum of the operator D(λ) is empty and that its eigenvalues may accumulate only at “thresholds” in the absolutely continuous spectrum. 相似文献
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Marijke De Soete 《Journal of Geometry》1987,29(1):50-60
In [2] we dealt with a characterization of the generalized quadrangle Q(4,q), q odd, by introducing the concept of (0,2)-set. The aim of this paper is to give a characterization of P(Q(4,q),L), q odd and L an arbitrary regular line of Q(4,q), by constructing these (0,2)-sets and using the result of [2]. 相似文献
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Tuo-Yeong Lee 《Journal of Mathematical Analysis and Applications》2008,340(1):53-63
We use a unified approach to obtain several integrability theorems of Boas [R.P. Boas, Integrability of trigonometric series, I, Duke Math. J. 18 (1951) 787-793]. In particular, we settle two conjectures of Móricz [F. Móricz, On the integrability of double cosine and sine series, II, J. Math. Anal. Appl. 154 (1991) 466-483] concerning double trigonometric series. 相似文献
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讨论了赋范空间中度量投影的收敛性.得到了在局部紧集控制下,Chebyshev凸集序列的度量投影的收敛性与K-M收敛,Wijsman收敛和Kuratowski收敛都等价.本文的结论完善了M.Tsukada在[1]和[2]结果. 相似文献
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Huanyin Chen 《代数通讯》2013,41(8):2517-2529
Let R be regular. We show that the following are equivalent:(1) R is a one sided unit regular ring. (2) For every x [euro] R, there exist an idempotente and a right or left invertible u such that x [d] eu or x [d] ue. (3) For every x [euro] R,there exists a right or left invertible u such that xu or ux is an idempotent. Moreover, we give some characterizations of one-sided unit regular rings by group inverses. 相似文献
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Forbidden hyperfine transitions are observed in the electron spin resonance spectrum of divalent Mn55 ion in NaCl single crystal for a particular associated pair. From the measurements of the M = + 1/2 → ?1/2, Δm = ± 1 transitions the parametersQ′ and Q″ of the nuclear electric quadrupole part of the spin-Hamiltonian Ho = Q′ [Iz 2 ? 1/3 I (I + 1)] + Q″ (Ix 2?Iy 2) are found to be + 1.70 × 10?4 cm.?1 and +0.16 × 10?4 cm.?1 respectively. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(10):1181-1184
We study the discrete spectrum arising in the spectral gaps of an elliptic periodic differential operator, P, perturbed by a differential operator, Q, with decaying coefficient. In the semi-classical regime (Q = Q(h), h0) (resp. the large-coupling constant: Q = λQ, λ → + ∞,), we obtain an asymptotic expansion in powers of h (resp. λ) of trƒ(P + Q(h)) (resp. trƒ(P + λQ)) and we give explicitly the leading term. Here ƒ ε C0∞(I) where I is an interval disjoint from the spectrum of P. We apply these results to study the asymptotic distribution of eigenvalues. 相似文献