Subspaces,angles and pairs of orthogonal projections

We give a new proof for the Wedin theorem on the simultaneous unitary similarity transformation of two orthogonal projections and show that it is equivalent to Halmos' theorem on the unitary equivalence of projection pairs. As a consequence of these theorems, we derive several results on pairs of orthogonal projections, relative subspace positions and oblique projections as well.     

Projections on tensor products of Banach spaces

We characterize norm hermitian operators on classes of tensor products of Banach spaces and derive results for the particular settings of injective and projective tensor products. We provide a characterization of bi-circular and generalized bi-circular projections on tensor products of Banach spaces supporting only dyadic surjective isometries. Received: 26 February 2007, Revised: 30 May 2007     

Trialitarian automorphisms of lie algebras

Over an algebraically closed field of characteristic zero simple Lie algebras admit outer automorphisms of order 3 if and only if they are of type D₄. Moreover, thereare two conjugacy classes of such automorphisms. Among orthogonal Lie algebras over arbitrary fields of characteristic zero, only orthogonal Lie algebras relative to quadratic norm forms of Cayley algebras admit outer automorphisms of order 3. We give a complete list of conjugacy classes of outer automorphisms of order 3 for orthogonal Lie algebras over arbitrary fields of characteristic zero. For the norm form of a given Cayley algebra, one class is associated with the Cayley algebra and the others with central simple algebras of degree 3 with involution of the second kind such that the cohomological invariant of the involution is the norm form.     

Fredholm Properties of the Difference of Orthogonal Projections in a Hilbert Space

Buckholtz (Proc. Amer. Math. Soc. 128 (2000), 1415–1418) gave necessary and sufficient conditions for the invertibility of the difference of two orthogonal projections in a Hilbert space. We generalize this result by investigating when the difference of such projections is a Fredholm operator, and give an explicit formula for its Fredholm inverse.     

On some norm equalities in pre-Hilbert C*-modules

We characterize when the norm of the sum of two elements in a pre-Hilbert C*-module equals the sum of their norms. We also give the necessary and sufficient conditions for two orthogonal elements of a pre-Hilbert C*-module to satisfy Pythagoras’ equality.     

凸性与度量投影的连续性

本文研究近强凸、近非常凸Banach空间中度量投影的连续性。获得如下结果：若A是近强凸（近非常凸）空间中的逼近凸集,则度量投影PA是范-范上半连续的（范-弱上半连续的）。此外,我们还利用度量投影的连续性给出Banach空间为近强凸、近非常凸的一些充分必要条件。     

Projectionless C*-algebras

We give a sufficient condition for a unital C*-algebra to have no nontrivial projections, and we apply this result to known examples and to free products. We also show how questions of existence of projections relate to the norm-connectedness of certain sets of operators.

     

Projections,reconstructions and orthogonal functions

The techniques used for reconstructing an object from its projections are set up within a general mathematical framework. We show that the simplest version of the problem involves choosing a generator for two sets of orthogonal functions, and we also give the general theory. We illustrate the power of the method by considering in detail four examples of special projections. We have done these calculations to tie together with a general theory the many different choices of orthogonal polynomial that have been used by various investigators in the problem of projection and reconstruction and to show, by specific illustration, the interconnection of these various functions.     

正压缩算子Jordan积的最大最小谱点

主要讨论了正压缩算子Jordan积的谱,刻画了正压缩算子Jordan积的最大最小谱点以及正交投影Jordan积的谱.     

Convergence properties of some block Krylov subspace methods for multiple linear systems

In the present paper, we give some convergence results of the global minimal residual methods and the global orthogonal residual methods for multiple linear systems. Using the Schur complement formulae and a new matrix product, we give expressions of the approximate solutions and the corresponding residuals. We also derive some useful relations between the norm of the residuals.     

Products of projections in von Neumann algebras

We describe the elements of von Neumann algebras which can be represented as products of orthogonal projections and idempotents, and estimate the minimal number of terms in the product.     

Convergence of non-periodic infinite products of orthogonal projections and nonexpansive operators in Hilbert space

We provide sufficient conditions for strong and uniform (on bounded subsets of initial points) convergence of infinite products of orthogonal projections and other (possibly nonlinear) nonexpansive operators in a Hilbert space. Our main tools are new estimates of the inclination of a finite tuple of closed linear subspaces.     

Commutants modulo the compact operators of certain CSL algebras II

The commutant modulo compacts, or essential commutant, of a reflexive algebra with commutative subspace lattice is a C^* algebra which is the sum of the compact operators in L(H) and a C^* subalgebra of the core. We give a characterization of the essential commutant of a separably acting CSL algebra in terms of properties of the spectral measure of an operator in the intersection of the essential commutant and the core. This is used to determine some sufficient conditions on the lattice for when the essential commutant is norm generated by the projections it contains.     

The Drazin inverses of products and differences of orthogonal projections

In this note, the Drazin inverses of products and differences of orthogonal projections on a Hilbert space are established.     

正交投影的积与差的Moore-Penrose逆

运用分块算子矩阵的方法,给出了HIlbert空间上两个正交投影的和与差的Moore-Penrose逆的一个新的表达式.     

Sharp estimates for the covering numbers of the Weierstrass fractal kernel

In this paper, we present sharp estimates for the covering numbers of the embedding of the reproducing kernel Hilbert space (RKHS) associated with the Weierstrass fractal kernel into the space of continuous functions. The method we apply is based on the characterization of the infinite-dimensional RKHS generated by the Weierstrass fractal kernel and it requires estimates for the norm operator of orthogonal projections on the RKHS.     

Decompositions in Quantum Logic

We present a method of constructing an orthomodular poset from a relation algebra. This technique is used to show that the decompositions of any algebraic, topological, or relational structure naturally form an orthomodular poset, thereby explaining the source of orthomodularity in the ortholattice of closed subspaces of a Hilbert space. Several known methods of producing orthomodular posets are shown to be special cases of this result. These include the construction of an orthomodular poset from a modular lattice and the construction of an orthomodular poset from the idempotents of a ring.

Particular attention is paid to decompositions of groups and modules. We develop the notion of a norm on a group with operators and of a projection on such a normed group. We show that the projections of a normed group with operators form an orthomodular poset with a full set of states. If the group is abelian and complete under the metric induced by the norm, the projections form a -complete orthomodular poset with a full set of countably additive states.

We also describe some properties special to those orthomodular posets constructed from relation algebras. These properties are used to give an example of an orthomodular poset which cannot be embedded into such a relational orthomodular poset, or into an orthomodular lattice. It had previously been an open question whether every orthomodular poset could be embedded into an orthomodular lattice.

     

加权变指标Herz-Morrey空间上的双线性Hardy算子的交换子

本文利用权范数给出BMO函数的一个新刻画.作为此刻画的一个应用,获得了双线性Hardy算子和BMO函数生成的交换子在加权变指标Herz-Morrey乘积空间上的有界性.     

Products of integral-type operators and composition operators from the mixed norm space to Bloch-type spaces

Siberian Mathematical Journal - We give a complete picture of the boundedness and compactness of the products of integral-type operators and composition operators from the mixed norm space to...     

Projection theorems in hyperbolic space

We establish Marstrand-type projection theorems for orthogonal projections along geodesics onto m-dimensional subspaces of the hyperbolic n-space by a geometric argument. Moreover, we obtain a Besicovitch–Federer type characterization of purely unrectifiable sets in terms of these hyperbolic orthogonal projections.