共查询到20条相似文献,搜索用时 31 毫秒
1.
LetX andY denote two complex Banach spaces and letB(Y, X) denote the algebra of all bounded linear operators fromY toX. ForA∈B(X)
n
,B∈B(Y)
n
, the elementary operator acting onB(Y, X) is defined by
. In this paper we obtain the formulae of the spectrum and the essential spectrum of Δ(A, B) by using spectral mapping theorems. Forn=1, we prove thatS
p
(L
A
,R
B
)=σ(A)×σ(B) and
. 相似文献
2.
Zejun Huang 《Linear algebra and its applications》2011,434(2):457-462
We prove the spectral radius inequality ρ(A1°A2°?°Ak)?ρ(A1A2?Ak) for nonnegative matrices using the ideas of Horn and Zhang. We obtain the inequality ‖A°B‖?ρ(ATB) for nonnegative matrices, which improves Schur’s classical inequality ‖A°B‖?‖A‖‖B‖, where ‖·‖ denotes the spectral norm. We also give counterexamples to two conjectures about the Hadamard product. 相似文献
3.
Ji-ming Guo 《应用数学学报(英文版)》2008,24(2):289-296
In this paper, sharp upper bounds for the Laplacian spectral radius and the spectral radius of graphs are given, respectively. We show that some known bounds can be obtained from our bounds. For a bipartite graph G, we also present sharp lower bounds for the Laplacian spectral radius and the spectral radius, respectively. 相似文献
4.
Walks and the spectral radius of graphs 总被引:1,自引:0,他引:1
Vladimir Nikiforov 《Linear algebra and its applications》2006,418(1):257-268
Given a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its clique number, and wk(G) for the number of its k-walks. We prove that the inequalities
5.
This paper contains a connected account of results concerning the maximum problem raised by the first-named author in [21] and of its generalizations. For a number of results simplified proofs are given, new estimates are obtained, and important connections with stability theory and with classical function theory are pointed out. 相似文献
6.
Thomas Hawkins 《Historia Mathematica》1975,2(1):1-29
It is well-known that Cauchy (1829) provided the first general proof that the eigenvalues of a symmetric matrix are real. Furthermore, Cauchy's paper initiated the developments that resulted in the creation of a substantial spectral theory of matrices by the early 1870's. The following essay relates Cauchy's work and its historical significance to the consideration of eigenvalue problems during the 18th century. 相似文献
7.
M. Thamban Nair 《Numerical Functional Analysis & Optimization》2013,34(9-10):1019-1037
Stewart (1971) and Demmel (1987) have proposed iterative procedures for refining invariant subspaces of Hilbert space operators and matrices respectively. In this paper, modifications are proposed for these procedures which facilitates their application to bounded Banach space operators. Under regularity conditions (which could include densely defined closed operators) it is shown that the modifications perform as well as or better than the procedures of Stewart and Demmel. 相似文献
8.
In this paper we characterize all nxn matrices whose spectral radius equals their spectral norm. We show that for n?3 the class of these matrices contains the normal matrices as a subclass. 相似文献
9.
Summary Conditions have been given [7] under which a special automorphism over an automorphism admitting a simple approximation again admits a simple approximation, and so has simple spectrum.In this paper using different techniques to those employed in [7], we obtain improved results in the same direction. Specifically, conditions are given for a special automorphism over an automorphism, which admits either a simple approximation, or an approximation with suitable speed, to have bounded spectral multiplicity. Furthermore, we obtain as a corollary a result on primitive automorphisms, which partially generalises a result appearing in [4]. 相似文献
10.
Thomas Brélivet 《Bulletin des Sciences Mathématiques》2002,126(4):333-342
Using the theory of the mixed Hodge structure one can define a notion of spectrum of a singularity or of a polynomial. Recently Claus Hertling proposed a conjecture about the variance of the spectrum of a singularity. Alexandru Dimca proposed a similar conjecture on polynomials. Here, we prove these two conjectures in the case of dimension 2 and when the singularity or the polynomial is Newton non-degenerated and commode. 相似文献
11.
Martin Fürer 《Linear algebra and its applications》2010,432(9):2373-2380
We extend the traditional spectral invariants (spectrum and angles) by a stronger polynomial time computable graph invariant based on the angles between projections of standard basis vectors into the eigenspaces (in addition to the usual angles between standard basis vectors and eigenspaces). The exact power of the new invariant is still an open problem. We also define combinatorial invariants based on standard graph isomorphism heuristics and compare their strengths with the spectral invariants. In particular, we show that a simple edge coloring invariant is at least as powerful as all these spectral invariants. 相似文献
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Braxton Osting 《Applied Mathematics Letters》2012,25(11):1926-1930
Periodic media are routinely used in optical devices and, in particular, photonic crystals to create spectral gaps, prohibiting the propagation of waves with certain temporal frequencies. In one dimension, Bragg structures, also called quarter-wave stacks, are frequently used because they are relatively easy to manufacture and the spectrum exhibits large spectral gaps at explicitly computable frequencies. In this short work, we use variational methods to demonstrate that within an admissible class of pointwise-bounded, periodic media, the Bragg structure uniquely maximizes the first spectral gap-to-midgap ratio. 相似文献
15.
Amin Boumenir 《Journal of Fourier Analysis and Applications》1999,5(4):373-383
We are interested in finding necessary and sufficient conditions for irregular sampling to hold. We shall show that the inverse spectral problem can be used to construct sampling type theorems from the knowledge of the sampling points only. This improves Kramer's theorem as it reveals all possible distributions of the sampling points together with a construction of the sampling functions. 相似文献
16.
D. A. Gulyaev 《Differential Equations》2011,47(10):1520-1524
We study the uniform convergence, on a closed interval, of spectral expansions of Hölder functions in a given complete and minimal system of eigenfunctions corresponding to a spectral problem with spectral parameter in a boundary condition. We consider boundary conditions of the third kind and subject the function to be expanded to a condition of nonlocal type ensuring the uniform convergence. We prove a theorem stating that expansions in the entire system of eigenfunctions of the problem are possible without any additional conditions. 相似文献
17.
Mathematical Notes - In this paper, both well-known and new properties of the spectral abscissa and the logarithmic norm are described. In addition to well-known formulas for the norm of a matrix... 相似文献
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Barry Simon 《Proceedings of the American Mathematical Society》1998,126(5):1409-1413
We provide a new proof of a theorem of Birman and Solomyak that if with trace class and , then , where is the Krein spectral shift from to . Our main point is that this is a simple consequence of the formula .