Search results for " Algebra"
showing 10 items of 2082 documents
A space of projections on the Bergman space
2010
We define a set of projections on the Bergman space A 2 , which is parameterized by an ane subset of a Banach space of holomorphic functions in the disk and which includes the classical Forelli-Rudin projections.
Closedness and lower semicontinuity of positive sesquilinear forms
2009
The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.
Unconditional Basis and Gordon–Lewis Constants for Spaces of Polynomials
2001
Abstract No infinite dimensional Banach space X is known which has the property that for m ⩾2 the Banach space of all continuous m -homogeneous polynomials on X has an unconditional basis. Following a program originally initiated by Gordon and Lewis we study unconditionality in spaces of m -homogeneous polynomials and symmetric tensor products of order m in Banach spaces. We show that for each Banach space X which has a dual with an unconditional basis ( x * i ), the approximable (nuclear) m -homogeneous polynomials on X have an unconditional basis if and only if the monomial basis with respect to ( x * i ) is unconditional. Moreover, we determine an asymptotically correct estimate for the …
Unbounded C*-seminorms and biweights on partial *-algebras
2005
Unbounded C*-seminorms generated by families of biweights on a partial *-algebra are considered and the admissibility of biweights is characterized in terms of unbounded C*-seminorms they generate. Furthermore, it is shown that, under suitable assumptions, when the family of biweights consists of all those ones which are relatively bounded with respect to a given C*-seminorm q, it can be obtained an expression for q analogous to that one which holds true for the norm of a C*-algebra.
A short proof of a theorem of Juhasz
2011
Abstract We give a simple proof of the increasing strengthening of Arhangelʼskii Theorem. Our proof naturally leads to a refinement of this result of Juhasz.
THE STRUCTURE OF MUTUALLY PERMUTABLE PRODUCTS OF FINITE NILPOTENT GROUPS
2007
We consider mutually permutable products G = AB of two nilpotent groups. The structure of the Sylow p-subgroups of its nilpotent residual is described.
Complete, exact, and efficient computations with cubic curves
2004
The Bentley-Ottmann sweep-line method can be used to compute thearrangement of planar curves provided a number of geometricprimitives operating on the curves are available. We discuss themathematics of the primitives for planar algebraic curves of degreethree or less and derive efficient realizations. As a result, weobtain a complete, exact, and efficient algorithm for computingarrangements of cubic curves. Conics and cubic splines are specialcases of cubic curves. The algorithm is complete in that it handles all possibledegeneracies including singularities. It is exact in that itprovides the mathematically correct result. It is efficient in thatit can handle hundreds of curves with a quart…
Rank structured approximation method for quasi--periodic elliptic problems
2016
We consider an iteration method for solving an elliptic type boundary value problem $\mathcal{A} u=f$, where a positive definite operator $\mathcal{A}$ is generated by a quasi--periodic structure with rapidly changing coefficients (typical period is characterized by a small parameter $\epsilon$) . The method is based on using a simpler operator $\mathcal{A}_0$ (inversion of $\mathcal{A}_0$ is much simpler than inversion of $\mathcal{A}$), which can be viewed as a preconditioner for $\mathcal{A}$. We prove contraction of the iteration method and establish explicit estimates of the contraction factor $q$. Certainly the value of $q$ depends on the difference between $\mathcal{A}$ and $\mathcal…
Ordinary and graded cocharacter of the Jordan algebra of 2x2 upper triangular matrices
2014
Abstract Let F be a field of characteristic zero and U J 2 ( F ) be the Jordan algebra of 2 × 2 upper triangular matrices over F . In this paper we give a complete description of the space of multilinear graded and ordinary identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . For every Z 2 -grading of U J 2 ( F ) we compute the multiplicities in the graded cocharacter sequence and furthermore we compute the ordinary cocharacter.
Transportation cost inequalities on path and loop groups
2005
AbstractLet G be a connected Lie group with the Lie algebra G. The action of Cameron–Martin space H(G) on the path space Pe(G) introduced by L. Gross (Illinois J. Math. 36 (1992) 447) is free. Using this fact, we define the H-distance on Pe(G), which enables us to establish a transportation cost inequality on Pe(G). This method will be generalized to the path space over the loop group Le(G), so that we obtain a transportation cost inequality for heat measures on Le(G).