查看更多>>摘要：We give the complete description of bijective real-linear transformations on B(H), the algebra of all bounded linear operators on an infinite-dimensional complex Hilbert space H, where every unitary U is an element of B(H) is mapped to a unitary phi(U). In turn, bijective real-linear maps on B(H) preserving equivalence by unitaries will be determined. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper we introduce a new probabilistic model for the occurrence of erasures in multiple channel data transmission. It uses Parseval frames to encode the information to be transmitted. Information loss in the transmission channels is modeledby a sequence of Bernoulli random variables. Our model gives insights on the probabilistic properties of the channels and allows us to find optimal Parseval frames that minimize the lost of data in the worst one erasure case. We show also that compared to existing models [3,4,7,8], our optimal Parseval frames give better performance for recovering transmitted data. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we describe the relationship between the Perron root and eigenvectors of an irreducible subshift of finite type with the correlation between the forbidden words in the subshift. In particular, we derive an expression for the Perron eigenvectors of the associated adjacency matrix. As an application, we obtain the Perron eigenvectors for irreducible (0, 1) matrices which are adjacency matrices for directed graphs. Moreover, we derive an alternate definition of the Parry measure in ergodic theory on an irreducible subshift of finite type. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We study a finite (discrete) group Gthrough the information we obtain from P-1(G)={<pi(.)xi,xi > : pi : G -> U(H) isunitary, xi is an element of H, parallel to xi parallel to = 1} of norm one positive definite functions of G, arising from matrix coefficients of any unitary representation p. Below we summarize our results. (a) Knowing P-1(G) as a set of functions, when Gis a finite abelian group we can determine G congruent to Pi(j)Z(pjrj) as a direct product of its cyclic subgroups of prime power orders. (b) Knowing P-1(G) as a multiplicative semigroup, we can construct the subgroup lattice L(G) of G. With L(G) in stock, we can tell if G is cyclic, simple, perfect, solvable, supersolvable, or nilpotent. When G' is a finite simple group with P-1(G') congruent to P-1(G) as multiplicative semigroups, we show that G' congruent to Gas groups. (c) Knowing P-1(G) as a compact convex set, we can construct the group von Neumann algebra vN(G) of G' Consequently, when G' is another finite group with P-1(G) congruent to P-1(G') as convex sets, we show that vN(G) congruent to vN(G') as von Neumann algebras. In particular, we can tell if G is abelian. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital C*-algebras, with a particular focus on gapped maps for which the transient portion of the arising dynamical system can be separated from the persistent one. After some general results, we first devote our attention to the abelian case by investigating the unital *-endomorphisms of, in general nonunital, C*-algebras, and their spectral structure. The finitedimensional case is also investigated in detail, and examples are provided of unital completely positive maps for which the persistent part of the associated dynamical system is equipped with the new product making it into a C*-algebra, and the map under consideration restricts to a unital *-automorphism for this new C*-structure, thus generating a conservative dynamics on that persistent part. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：A nut graph is a simple graph whose adjacency matrix has the eigenvalue 0 with multiplicity 1 such that its corresponding eigenvector has no zero entries. Motivated by a question of Fowler et al. (2020) [5] to determine the pairs (n, d) for which a vertex-transitive nut graph of order n and degree d exists, Basic et al. (2021) [1] initiated the study of circulant nut graphs. Here we first show that the generator set of a circulant nut graph necessarily contains equally many even and odd integers. Then we characterize circulant nut graphs with the generator set {x, x + 1, x + 2,..., x + 2t - 1} for x, t is an element of N, which generalizes the result of Basic et al. for the generator set {1, 2, 3,..., 2t}. We further study circulant nut graphs with the generator set {1, 2, 3,..., 2t + 1} \ {t}, which yields nut graphs of every even order n >= 4t + 4 whenever t is odd such that t not equivalent to(10) 1 and t not equivalent to(18) 15. This fully resolves Conjecture 9 from Basic et al. (2021) [1]. We also study the existence of 4t-regular circulant nut graphs for small values of t, which partially resolves Conjecture 10 of Basic et al. (2021) [1]. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is a new representation result for analytic functions, in terms of composition and multiplication operators associated with a given rational function. Applications to the theory of de Branges-Rovnyak spaces, also in the indefinite metric setting, are given. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We prove that the triangular matrix algebra Lambda = ((H)(H) (0)(H)) is an affine quasi-hereditary algebra if and only if H is an affine quasi-hereditary algebra. Moreover, the category of Delta-good Lambda-modules, the global dimension and the characteristic tilting module of Lambda are described by using the corresponding ones of H. In the appendix, we prove that certain centralizer algebra and quotient algebra of an affine quasi-hereditary algebra are affine quasi-hereditary. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Let A be an n x n matrix. The Hermitian parts of A are denoted by R(A) = (A + A*)/2and J(A) = (A - A*)/(2i). The kernel vectors of the linear pencil xR(A) + yJ(A) + zI(n) play a role for the inverse numerical range of A. This kernel vector technique was applied to perform the inverse numerical range of 3 x3 symmetric matrices. In this paper, we follow the kernel vector method and apply the Abel theorem for 3 x3 Hermitian matrices. We present the elliptic curve group structure of the cubic curve associated to the ternary form of the matrix, and characterize the Abel type additive structure of the divisors of the cubic curve. A numerical example is given to illustrate the characterization related to the Riemann theta representation. (C) 2021 Elsevier Inc. All rights reserved.
Esteban, GuillermoHuemer, ClemensSilveira, Rodrigo, I
37页
查看更多>>摘要：We use production matrices to count several classes of geometric graphs. We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another, simple and elegant, way of counting the number of such objects. Counting geometric graphs is then equivalent to calculating the powers of a production matrix. Applying the technique of Riordan Arrays to these production matrices, we establish new formulas for the numbers of geometric graphs as well as combinatorial identities derived from the production matrices. Further, we obtain the characteristic polynomial and the eigenvectors of such production matrices. (C) 2021 Elsevier Inc. All rights reserved.
NSTL
Elsevier