Showing papers on "Dual norm published in 1991"
TL;DR: In this article, the authors lay the foundations for a systematic study of tensor products of subspaces of C∗-algebras and employ various notions of duality.
311 citations
24 citations
22 citations
11 citations
TL;DR: In this paper, a study of normed linear relations with emphasis on results and properties that do not necessarily hold, or have no counterparts, for arbitrary normed convex processes is presented, and sufficient conditions are given under which the norm of a linear relation M is equal to some operator part (i.e., a single-valued linear selection) of M.
8 citations
26 Jun 1991
TL;DR: The modified Newton method for constrained optimization in Banach space is studied, and a new algorithm for solving state-constrained optimal control problems is proposed by applying the generalized dual quasi-Newton method.
Abstract: We study the modified Newton method for constrained optimization in Banach space, and generalize the dual quasi-Newton algorithm to Hilbert space. A new algorithm for solving state-constrained optimal control problems is proposed by applying the generalized dual quasi-Newton method.
4 citations
TL;DR: In this paper, it was shown that the dual norms of a tame nuclear Frechet space are logarithmically convex and thus the tame splitting condition (ΩDZ) is equivalent to the topological condition of D. Vogt and M. J. Wagner, and the splitting theorem has been proved for the kernels of any hypoelliptic system of linear partial differential operators with constant coefficients on a bounded convex region in ℝN.
Abstract: In a previous paper, the quotient spaces of (s) in the tame category of nuclear Frechet spaces have been characterized by property (ΩDZ) corresponding to the topological condition (Ω) of D. Vogt and M. J. Wagner. In addition, a splitting theorem has been proved which provides the existence of a tame linear right inverse of a tame linear map on the assumption that the kernel of the given map has property (ΩDZ) and that certain tameness conditions hold. In this paper it is proved that property (Ω) in standard form (i.e., the dual norms ‖ ‖n* are logarithmically convex) implies the tame splitting condition (ΩDZ) for any tamely nuclear Frechet space equipped with a grading defined by sermiscalar products. As an application, property (ΩDZ) is verified for the kernels of any hypoelliptic system of linear partial differential operators with constant coefficients on ℝN or on a bounded convex region in ℝN.
3 citations
01 Jan 1991
TL;DR: Norms are widespread in the techniques of uncertain modelling and robust control and most of the important relations for norms are listed or derived in this chapter.
Abstract: Norms are widespread in the techniques of uncertain modelling and robust control. Multivariable systems and the state-space representation require valuating vectors and matrices by a single number. Most of the important relations for norms are listed or derived in this chapter. This material may be considered as a kind of reference, and the chapter may be skipped when the reader is already familiar with this subject.
2 citations
1 citations
01 Jan 1991
TL;DR: In this paper, the minimum norm control problem for distributed parameter systems in Banach spaces is studied, and it is shown that theminimum norm control may be represented in a formal way when the input space is reflexive, smooth and strictly convex.
Abstract: In this paper,the minimum norm control problems for distributed parameter systems inBanach spaces are studied.By the method of geometry in Banach space,it is shown that theminimum norm control may be represented in a formal way wheneyer the input space is re-flexive,smooth and strictly convex;thus,the analysis anl calculation of the minimum normcontrol becomes easy with the formal representation.
01 Jan 1991
TL;DR: In this paper, the authors developed an efficient algorithm for computing the norm of Tsirelson space T, a reflexive Banach space containing no isomorphic copies of any l p space.
Abstract: After a review of Tsirelson space T, a reflexive Banach space containing no isomorphic copies of any l p space, the authors develop an efficient algorithm for computing the norm of T. Properties of the algorithm, timings, and space considerations are discussed.
26 Jun 1991
TL;DR: A fast algorithm is presented to compute the L∞-norm for generalized state space representations of continuous and discrete-time systems using the relation between the singular values of the transfer function matrix and the eigenvalues of a related Hamiltonian matrix.
Abstract: A fast algorithm is presented to compute the L∞-norm for generalized state space representations of continuous and discrete-time systems. The L∞-norm of a generalized discrete time system is dircetly caclulated without having recourse to a bilinear transformation. The algorithm is based on the relation between the singular values of the transfer function matrix and the eigenvalues of a related Hamiltonian matrix. The norm is computed with guaranteed accuracy.