共查询到20条相似文献,搜索用时 62 毫秒
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A. M. Bikchentaev 《Theoretical and Mathematical Physics》2018,195(1):557-562
Let ? be a trace on the unital C*-algebra A and M ? be the ideal of the definition of the trace ?. We obtain a C*analogue of the quantum Hall effect: if P,Q ∈ A are idempotents and P ? Q ∈ M ? , then ?((P ? Q)2n+1) = ?(P ? Q) ∈ R for all n ∈ N. Let the isometries U ∈ A and A = A*∈ A be such that I+A is invertible and U-A ∈ M ? with ?(U-A) ∈ R. Then I-A, I?U ∈ M ? and ?(I?U) ∈ R. Let n ∈ N, dimH = 2n + 1, the symmetry operators U, V ∈ B(H), and W = U ? V. Then the operator W is not a symmetry, and if V = V*, then the operator W is nonunitary. 相似文献
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Define the incremental fractional Brownian field Z_H(τ,s)=B_H(s+τ)-B_H(s),where B_H(s) is a standard fractional Brownian motion with Hurst parameter H ∈(0,1).In this paper,we first derive an exact asymptotic of distribution of the maximum M_H(T_u)=sup_τ∈[0,1],s∈[0,xT_u]Z_H(τ,s),which holds uniformly for x ∈[A,B]with A,B two positive constants.We apply the findings to analyse the tail asymptotic and limit theorem of MH(τ) with a random index τ.In the end,we also prove an ahnost sure limit theorem for the maximum M_(1/2)(T) with non-random index T. 相似文献
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In earlier papers, for “large” (but otherwise unspecified) subsets A, B of Z p and for h(x) ∈ Z p [x], Gyarmati studied the solvability of the equations a + b = h(x), resp. ab = h(x) with a ∈ A, b ∈ B, x ∈ Z p , and for large subsets A, B, C, D of Z p Sárközy showed the solvability of the equations a + b = cd, resp. ab + 1 = cd with a ∈ A, b ∈ B, c ∈ C, d ∈ D. In this series of papers equations of this type will be studied in finite fields. In particular, in Part I of the series we will prove the necessary character sum estimates of independent interest some of which generalize earlier results. 相似文献
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Alain Escassut 《P-Adic Numbers, Ultrametric Analysis, and Applications》2017,9(2):138-143
Let K be an ultrametric complete algebraically closed field, let D be a disk {x ∈ K ‖x| < R} (with R in the set of absolute values of K) and let A be the Banach algebra of bounded analytic functions in D. The vector space generated by the set of characters of A is dense in the topological dual of A if and only if K is not spherically complete. Let H(D) be the Banach algebra of analytic elements in D. The vector space generated by the set of characters of H(D) is never dense in the topological dual of H(D). 相似文献
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A criterion for the classification of Bott towers is presented, i.e., two Bott towers B *(A) and B *(A′) are isomorphic if and only if the matrices A and A′ are equivalent. The equivalence relation is defined by two operations on matrices. And it is based on the observation that any Bott tower B *(A) is uniquely determined by its structure matrix A, which is a strictly upper triangular integer matrix. The classification of Bott towers is closely related to the cohomological rigidity problem for both Bott towers and Bott manifolds. 相似文献
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For a normed algebra A and natural numbers k we introduce and investigate the ∥ · ∥ closed classes P k (A). We show that P1(A) is a subset of P k (A) for all k. If T in P1(A), then Tn lies in P1(A) for all natural n. If A is unital, U, V ∈ A are such that ∥U∥ = ∥V∥ = 1, VU = I and T lies in P k (A), then UTV lies in P k (A) for all natural k. Let A be unital, then 1) if an element T in P1(A) is right invertible, then any right inverse element T?1 lies in P1(A); 2) for ßßIßß = 1 the class P1(A) consists of normaloid elements; 3) if the spectrum of an element T, T ∈ P1(A) lies on the unit circle, then ∥TX∥ = ∥X∥ for all X ∈ A. If A = B(H), then the class P1(A) coincides with the set of all paranormal operators on a Hilbert space H. 相似文献
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The system where v = C*x is an output, u = S*y is a control, A(·) ∈ R n × n , B(·) ∈ R n × (n–p), C ∈ R n × (n–p), and D ∈ R n × (n–p), is considered. The elements αij(·) and βij(·) of the matrices A(·) and B(·) are arbitrary functionals satisfying the conditions It is assumed that A(·) ∈ Z 1 ∪ Z 3 and A*(·) ∈ Z 1 ∪ Z 3, where Z 1 is the class of matrices in which the first p elements of the kth superdiagonal are sign-definite and the elements above them are sufficiently small. The class Z 3 differs from Z t1 in that the elements between this superdiagonal and the (k + 1)th row are sufficiently small. If k > p, then the elements of the p × p square in the upper left corner of the matrix are sufficiently small as well. By using special quadratic Lyapunov functions, a matrix D for which y(t)–x(t) → 0 exponentially as t → ∞ is first found, and then a matrix S for which the vectors x(t) and y(t) have the same property is constructed.
相似文献
$$\frac{{dx}}{{dt}} = A\left( \cdot \right)x + B\left( \cdot \right)u,{\kern 1pt} \frac{{dy}}{{dt}} = A\left( \cdot \right)y + B\left( \cdot \right)u + D\left( {C*y - v} \right)$$
$$\mathop {\sup }\limits_{\left( \cdot \right)} |{\alpha _{ij}}\left( \cdot \right)| < \infty \left( {i,j \in 1,n} \right),\mathop {\sup }\limits_{\left( \cdot \right)} |{\beta _{ij}}\left( \cdot \right)| < \infty \left( {i \in 1,n,j \in 1,n - p} \right).$$
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The nonsoluble length λ(G) of a finite group G is defined as the minimum number of nonsoluble factors in a normal series of G each of whose quotients either is soluble or is a direct product of nonabelian simple groups. The generalized Fitting height of a finite group G is the least number h = h* (G) such that F* h (G) = G, where F* 1 (G) = F* (G) is the generalized Fitting subgroup, and F* i+1(G) is the inverse image of F* (G/F*i (G)). In the present paper we prove that if λ(J) ≤ k for every 2-generator subgroup J of G, then λ(G) ≤ k. It is conjectured that if h* (J) ≤ k for every 2-generator subgroup J, then h* (G) ≤ k. We prove that if h* (〈x, xg 〉) ≤ k for allx, g ∈ G such that 〈x, xg 〉 is soluble, then h* (G) is k-bounded. 相似文献
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For any module V over the two-dimensional non-abelian Lie algebra b and scalar α ∈ C, we define a class of weight modules F α (V) with zero central charge over the affine Lie algebra A 1 (1) . These weight modules have infinitedimensional weight spaces if and only if V is infinite dimensional. In this paper, we will determine necessary and sufficient conditions for these modules F α(V) to be irreducible. In this way, we obtain a lot of irreducible weight A 1 (1) -modules with infinite-dimensional weight spaces. 相似文献
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Tom Sanders 《Israel Journal of Mathematics》2010,179(1):1-28
A continuous linear map T from a Banach algebra A into another B approximately preserves the zero products if ‖T(a)T(b)‖ ≤ α‖a‖‖b‖ (a,b ∈ A, ab = 0) for some small positive α. This paper is mainly concerned with the question of whether any continuous linear surjective map T: A → B that approximately preserves the zero products is close to a continuous homomorphism from A onto B with respect to the operator norm. We show that this is indeed the case for amenable group algebras. 相似文献
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We show that for a linear space of operators M ? B(H1, H2) the following assertions are equivalent. (i) M is reflexive in the sense of Loginov-Shulman. (ii) There exists an order-preserving map Ψ = (ψ1, ψ2) on a bilattice Bil(M) of subspaces determined by M with P ≤ ψ1(P,Q) and Q ≤ ψ2(P,Q) for any pair (P,Q) ∈ Bil(M), and such that an operator T ∈ B(H1, H2) lies in M if and only if ψ2(P,Q)Tψ1(P,Q) = 0 for all (P,Q) ∈ Bil(M). This extends the Erdos-Power type characterization of weakly closed bimodules over a nest algebra to reflexive spaces. 相似文献
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M. S. Eryashkin 《Russian Mathematics (Iz VUZ)》2016,60(8):17-28
We extend several classical results in the theory of invariants of finite groups to the case of action of a finite-dimensional Hopf algebra H on an algebra satisfying a polynomial identity. In particular, we prove that an H-module algebra A over an algebraically closed field k is integral over the subalgebra of invariants, if H is a semisimple and cosemisimple Hopf algebra. We show that for char k > 0, the algebra Z\({\left( A \right)^{{H_0}}}\) is integral over the subalgebra of central invariants Z(A)H, where Z(A) is the center of algebra A, H0 is the coradical of H. This result allowed us to prove that the algebra A is integral over the subalgebra Z(A)H in some special case. We also construct a counterexample to the integrality of the algebra \({A^{{H_0}}}\) over the subalgebra of invariants AH for a pointed Hopf algebra over a field of non-zero characteristic. 相似文献
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E. Yu. Bunkova 《Proceedings of the Steklov Institute of Mathematics》2016,294(1):201-214
The article is devoted to the theory of elliptic functions of level n. An elliptic function of level n determines a Hirzebruch genus called an elliptic genus of level n. Elliptic functions of level n are also of interest because they are solutions of the Hirzebruch functional equations. The elliptic function of level 2 is the Jacobi elliptic sine function, which determines the famous Ochanine–Witten genus. It is the exponential of the universal formal group of the form F(u, v) = (u2 ? v2)/(uB(v) ? vB(u)), B(0) = 1. The elliptic function of level 3 is the exponential of the universal formal group of the form F(u, v) = (u2A(v) ? v2A(u))/(uA(v)2 ? vA(u)2), A(0) = 1, A″(0) = 0. In the present study we show that the elliptic function of level 4 is the exponential of the universal formal group of the form F(u, v) = (u2A(v) ? v2A(u))/(uB(v) ? vB(u)), where A(0) = B(0) = 1 and for B′(0) = A″(0) = 0, A′(0) = A1, and B″(0) = 2B2 the following relation holds: (2B(u) + 3A1u)2 = 4A(u)3 ? (3A12 ? 8B2)u2A(u)2. To prove this result, we express the elliptic function of level 4 in terms of the Weierstrass elliptic functions. 相似文献
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Let A be a standard Koszul standardly stratified algebra and X an A-module. The paper investigates conditions which imply that the module Ext* A (X) over the Yoneda extension algebra A* is filtered by standard modules. In particular, we prove that the Yoneda extension algebra of A is also standardly stratified. This is a generalization of similar results on quasi-hereditary and on graded standardly stratified algebras. 相似文献
16.
G. S. Mustafaev 《Functional Analysis and Its Applications》2007,41(3):241-244
Let A be a complex Banach algebra. It is well known that the second dual A** of A can be equipped with a multiplication that extends the original multiplication on A and makes A** a Banach algebra. We show that Rad(A) = ⊥(A * · A) and Rad(A **) = (A * · A)⊥ for some classes of Banach algebras A with scattered structure space. Some applications of these results are given. 相似文献
17.
Let G be a 2-edge-connected simple graph on n vertices. For an edge e = uv ∈ E(G), define d(e) = d(u) + d(v). Let F denote the set of all simple 2-edge-connected graphs on n ≥ 4 vertices such that G ∈ F if and only if d(e) + d(e’) ≥ 2n for every pair of independent edges e, e’ of G. We prove in this paper that for each G ∈ F, G is not Z 3-connected if and only if G is one of K 2,n?2, K 3,n?3, K 2,n?2 + , K 3,n?3 + or one of the 16 specified graphs, which generalizes the results of X. Zhang et al. [Discrete Math., 2010, 310: 3390–3397] and G. Fan and X. Zhou [Discrete Math., 2008, 308: 6233–6240]. 相似文献
18.
Let H 2 be Sweedler’s 4-dimensional Hopf algebra and r(H 2) be the corresponding Green ring of H 2. In this paper, we investigate the automorphism groups of Green ring r(H 2) and Green algebra F(H 2) = r(H 2)?? F, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r(H 2) is isomorphic to K 4, where K 4 is the Klein group, and the automorphism group of F(H 2) is the semidirect product of ?2 and G, where G = F {1/2} with multiplication given by a · b = 1? a ? b + 2ab. 相似文献
19.
Basudeb Dhara 《Czechoslovak Mathematical Journal》2018,68(1):95-119
Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, let F, G and H be three generalized derivations of R, I an ideal of R and f(x1,..., x n ) a multilinear polynomial over C which is not central valued on R. If for all r = (r1,..., r n ) ∈ I n , then one of the following conditions holds:
相似文献
$$F(f(r))G(f(r)) = H(f(r)^2 )$$
- (1)there exist a ∈ C and b ∈ U such that F(x) = ax, G(x) = xb and H(x) = xab for all x ∈ R
- (2)there exist a, b ∈ U such that F(x) = xa, G(x) = bx and H(x) = abx for all x ∈ R, with ab ∈ C
- (3)there exist b ∈ C and a ∈ U such that F(x) = ax, G(x) = bx and H(x) = abx for all x ∈ R
- (4)f(x1,..., x n )2 is central valued on R and one of the following conditions holds
- (a)there exist a, b, p, p’ ∈ U such that F(x) = ax, G(x) = xb and H(x) = px + xp’ for all x ∈ R, with ab = p + p’
- (b)there exist a, b, p, p’ ∈ U such that F(x) = xa, G(x) = bx and H(x) = px + xp’ for all x ∈ R, with p + p’ = ab ∈ C.
- (a)
20.
B. Davvaz L. K. Ardekani 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2017,52(4):166-174
In this paper, we introduce a new notion of generalized (Jordan) left derivation on rings as follows: let R be a ring, an additive mapping F : R → R is called a generalized (resp. Jordan) left derivation if there exists an element w ∈ R such that F(xy) = xF(y) + yF(x) + yxw (resp. F(x 2) = 2xF(x) + x 2 w) for all x, y ∈ R. Then, some related properties and results on generalized (Jordan) left derivation of square closed Lie ideals are obtained. 相似文献