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1.
We define the reduced minimum modulus
of a nonzero element a in a unital C
*-algebra
by
. We prove that
. Applying this result to
and its closed two side ideal
, we get that dist
,
and
for any
if RR
= 0, where
and
is the quotient homomorphism and
. These results generalize corresponding results in Hilbert spaces. 相似文献
2.
Lutz Strüngmann 《Archiv der Mathematik》2006,86(3):193-204
Let R be a unital associative ring and
two classes of left R-modules. In this paper we introduce the notion of a
In analogy to classical cotorsion pairs as defined by Salce [10], a pair
of subclasses
and
is called a
if it is maximal with respect to the classes
and the condition
for all
and
Basic properties of
are stated and several examples in the category of abelian groups are studied.
Received: 17 March 2005 相似文献
3.
The main result in Cossidente and Siciliano (J. Number Theory, Vol. 99 (2003) pp. 373–382) states that if a Singer subgroup of PGL(3,q) is an automorphism group of a projective, geometric
irreducible, non-singular plane algebraic curve
then either
or
. In the former case
is projectively equivalent to the curve
with equation Xq+1Y+Yq+1+X=0 studied by Pellikaan. Furthermore, the curve
has a very nice property from Finite Geometry point of view: apart from the three distinguished points fixed by the Singer
subgroup, the set of its
-rational points can be partitioned into finite projective planes
. In this paper, the full automorphism group of such curves is determined. It turns out that
is the normalizer of a Singer group in
. 相似文献
4.
Xiu Gui LIU 《数学学报(英文版)》2007,23(6):1025-1032
Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by (b0hn-h1bn-1)∈ ExtA^3,(p^n+p)q(Zp,Zp) in the Adams spectral sequence. At the same time, he proved that i.(hlhn) ∈ExtA^2,(p^n+P)q(H^*M, Zp) is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π(p^n+p)q-2M. In this paper, with Lin's results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq + sp^2q + spq + (s - 2)q + s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s+2,*-term of the Adams spectral sequence, where p ≥ 7, q = 2(p - 1), n ≥ 4 and 3 ≤ s 〈 p. 相似文献
5.
M. A. Bastos C. A. Fernandes Yu. I. Karlovich 《Integral Equations and Operator Theory》2006,55(1):19-67
We establish a symbol calculus for the C*-subalgebra
of
generated by the operators of multiplication by slowly oscillating and piecewise continuous functions and the operators
where
is the Cauchy singular integral operator and
The C*-algebra
is invariant under the transformations
where Uz is the rotation operator
Using the localtrajectory method, which is a natural generalization of the Allan-Douglas local principle to nonlocal type
operators, we construct symbol calculi and establish Fredholm criteria for the C*-algebra
generated by the operators
and
for the C*-algebra
generated by the operators
and
and for the C*-algebra
generated by the algebras
and
The C*-algebra
can be considered as an algebra of convolution type operators with piecewise slowly oscillating coefficients and shifts acting
freely. 相似文献
6.
Alina Iacob 《Archiv der Mathematik》2005,85(4):335-344
We consider two pairs of complete hereditary cotorsion theories
on the category of left R-modules, such that
We prove that for any left R-modules M, N and for any n ≧ 1, the generalized Tate cohomology modules
can be computed either using a left
of M and a left
of M or using a right
a right
of N.
Received: 17 December 2004 相似文献
7.
Birkhoff coordinates for KdV on phase spaces of distributions 总被引:1,自引:0,他引:1
The purpose of this paper is to extend the construction of Birkhoff coordinates for the KdV equation from the phase space
of square integrable 1-periodic functions with mean value zero to the phase space
of mean value zero distributions from the Sobolev space
endowed with the symplectic structure
More precisely, we construct a globally defined real-analytic symplectomorphism
where
is a weighted Hilbert space of sequences
supplied with the canonical Poisson structure so that the KdV Hamiltonian for potentials in
is a function of the actions
alone. 相似文献
8.
In this paper self-adjoint realizations in Hilbert and Pontryagin spaces of the formal expression
are discussed and compared. Here L is a positive self-adjoint operator in a Hilbert space
with inner product 〈·,·〉, α is a real parameter, and φ in the rank one perturbation is a singular element belonging to
with n ≥ 3, where
is the scale of Hilbert spaces associated with L in
相似文献
9.
Let
be a compact Riemannian manifold without boundary. In this paper, we consider the first nonzero eigenvalue of the p-Laplacian
and we prove that the limit of
when
is 2/d(M), where d(M) is the diameter of M. Moreover, if
is an oriented compact hypersurface of the Euclidean space
or
, we prove an upper bound of
in terms of the largest principal curvature κ over M. As applications of these results, we obtain optimal lower bounds of d(M) in terms of the curvature. In particular, we prove that if M is a hypersurface of
then:
.
Mathematics Subject Classifications (2000): 53A07, 53C21. 相似文献
10.
Oscar Perdomo 《Journal of Geometry》2006,84(1-2):100-105
In this paper we prove that if
is a closed minimal surface, then,
, for any homogeneous polynomial f of degree 3 with 0 a regular value of the function
. 相似文献
11.
We study sums of bisectorial operators on a Banach space X and show that interpolation spaces between X and D(A) (resp. D(B)) are maximal regularity spaces for the problem Ay + By = x in X. This is applied to the study of regularity properties of the evolution equation u′ + Au = f on
for
or
and the evolution equation u′ + Au = f on [0, 2π] with periodic boundary condition u(0) = u(2π) in
or
相似文献
12.
Let L and M be Archimedean vector lattices such that
and
are complex vector lattices. We constructively and intrinsically prove that if
is an order bounded disjointness preserving operator from
into
then the modulus
of
exists in the ordered vector space of all order bounded operators from L into M.
Received February 11, 2005; accepted in final form March 8, 2005. 相似文献
13.
Naser Zamani 《Archiv der Mathematik》2006,86(4):321-330
Let
be a homogeneous Noetherian ring with local base ring (R0,m0) and let M,N be two finitely generated graded R-modules. Let
denote the i-th graded generalized local cohomology of N relative to M with support in
. We study the vanishing, tameness and asymptotical stability of the homogeneous components of
.
Received: 22 March 2005; revised: 25 June 2005 相似文献
14.
Antonio G. García Miguel A. Hernández-Medina 《Mediterranean Journal of Mathematics》2005,2(3):345-356
Let
be a symmetric operator with compact resolvent defined in a Hilbert space
For any fixed
we consider an entire
function Ka which involves the resolvent of
Associated with Ka we obtain, by duality in
a Hilbert space
of entire functions which becomes a De Branges space of entire functions. This property provides a characterization of
regardless of the anti-linear mapping which has
as its range space. There exists also a sampling formula allowing to recover any function in
from its samples at the sequence of eigenvalues of
This work has been supported by the grant BFM2003–01034 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología. 相似文献
15.
Let Φ be an irreducible crystallographic root system with Weyl group W and coroot lattice
, spanning a Euclidean space V. Let m be a positive integer and
be the arrangement of hyperplanes in V of the form
for
and
. It is known that the number
of bounded dominant regions of
is equal to the number of facets of the positive part
of the generalized cluster complex associated to the pair
by S. Fomin and N. Reading.
We define a statistic on the set of bounded dominant regions of
and conjecture that the corresponding refinement of
coincides with the $h$-vector of
. We compute these refined numbers for the classical root systems as well as for all root systems when m = 1 and verify the conjecture when Φ has type A, B or C and when m = 1. We give several combinatorial interpretations to these numbers in terms of chains of order ideals in the root poset of Φ,
orbits of the action of W on the quotient
and coroot lattice points inside a certain simplex, analogous to the ones given by the first author in the case of the set
of all dominant regions of
. We also provide a dual interpretation in terms of order filters in the root poset of Φ in the special case m = 1.
2000 Mathematics Subject Classification Primary—20F55; Secondary—05E99, 20H15 相似文献
16.
This paper deals with a class
of pseudorandom bit generators – modified alternating
–generators. This class is constructed similarly to the class
of alternating step generators. Three subclasses of
are distinguished, namely linear, mixed and nonlinear generators. The main attention is devoted to the subclass
of linear and mixed generators generating periodic sequences with maximal period lengths. A necessary and sufficient condition for all sequences generated by the linear generators of
to be with maximal period lengths is formulated. Such sequences have good statistical properties, such as distribution of zeroes and ones, and large linear complexity. Two methods of cryptanalysis of the proposed generators are given. Finally, three new classes of modified alternating
–generators, designed especially to be more secure, are presented. 相似文献
17.
Xiu Gui LIU 《数学学报(英文版)》2007,23(3):385-392
In this paper, some groups Ext A^s.t (Zp, Zp) with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πpnq+(s+3)pq+(s+1)q-5S which is represented (up to a nonzero scalar) by β+2bohh∈ExtA^s+5,P^nq+(n+3)pq+(n+1)q+s(Zp, Zp) in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2(p - 1). 相似文献
18.
Christian Richter 《Journal of Geometry》2006,84(1-2):117-132
Let
be a group of affine transformations of the Euclidean plane
. Two topological discs D,
are called congruent by dissection with respect to
if D can be dissected into a finite number of subdiscs that can be rearranged by maps from
to a dissection of E.
Our main result says in particular that
admits congruence by dissection of any circular disc C with any square S if and only if
contains a contractive map and all orbits
,
, are dense in
. In this case any two discs D and E are congruent by dissection with respect to
and every disc D is congruent by dissection with n copies of D for every n ≥ 2.
Moreover, we give estimates on minimal numbers of pieces that are needed to realize congruences by dissection.
Dedicated to Irmtraud Stephani on the occasion of her 70th birthday 相似文献
19.
Let
be a continuous semimartingale and let
be a continuous function of bounded variation. Setting
and
suppose that a continuous function
is given such that F is C1,2 on
and F is
on
. Then the following change-of-variable formula holds:
where
is the local time of X at the curve b given by
and
refers to the integration with respect to
. A version of the same formula derived for an Itô diffusion X under weaker conditions on F has found applications in free-boundary problems of optimal stopping. 相似文献
20.
Let
be a family of unit balls in
with the property that the mutual distances of the centers are at least
. If any n2 members of
have a common line transversal, then
has a line transversal too.
Received: 27 January 2005; revised: 17 October 2005 相似文献