Search results for "Functional analysis"
showing 10 items of 1059 documents
Strongly extreme points and approximation properties
2017
We show that if $x$ is a strongly extreme point of a bounded closed convex subset of a Banach space and the identity has a geometrically and topologically good enough local approximation at $x$, then $x$ is already a denting point. It turns out that such an approximation of the identity exists at any strongly extreme point of the unit ball of a Banach space with the unconditional compact approximation property. We also prove that every Banach space with a Schauder basis can be equivalently renormed to satisfy the sufficient conditions mentioned. In contrast to the above results we also construct a non-symmetric norm on $c_0$ for which all points on the unit sphere are strongly extreme, but …
Polyhedrality and decomposition
2018
Abstract The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder basis or an uncountable unconditional basis, easier and more transparent. The hypotheses of both results are based on decomposing the unit sphere of a Banach space into countably many pieces, such that each one satisfies certain properties. Some examples of spaces having equivalent polyhedral norms are given.
On Daugavet indices of thickness
2020
Inspired by R. Whitley's thickness index the last named author recently introduced the Daugavet index of thickness of Banach spaces. We continue the investigation of the behavior of this index and also consider two new versions of the Daugavet index of thickness, which helps us solve an open problem which connect the Daugavet indices with the Daugavet equation. Moreover, we will improve the formerly known estimates of the behavior of Daugavet index on direct sums of Banach spaces by establishing sharp bounds. As a consequence of our results we prove that, for every $0<\delta<2$, there exists a Banach space where the infimum of the diameter of convex combinations of slices of the unit ball i…
On holomorphic functions attaining their norms
2004
Abstract We show that on a complex Banach space X , the functions uniformly continuous on the closed unit ball and holomorphic on the open unit ball that attain their norms are dense provided that X has the Radon–Nikodym property. We also show that the same result holds for Banach spaces having a strengthened version of the approximation property but considering just functions which are also weakly uniformly continuous on the unit ball. We prove that there exists a polynomial such that for any fixed positive integer k , it cannot be approximated by norm attaining polynomials with degree less than k . For X=d ∗ (ω,1) , a predual of a Lorentz sequence space, we prove that the product of two p…
Diameter 2 properties and convexity
2015
We present an equivalent midpoint locally uniformly rotund (MLUR) renorming $X$ of $C[0,1]$ on which every weakly compact projection $P$ satisfies the equation $\|I-P\| = 1+\|P\|$ ($I$ is the identity operator on $X$). As a consequence we obtain an MLUR space $X$ with the properties D2P, that every non-empty relatively weakly open subset of its unit ball $B_X$ has diameter 2, and the LD2P+, that for every slice of $B_X$ and every norm 1 element $x$ inside the slice there is another element $y$ inside the slice of distance as close to 2 from $x$ as desired. An example of an MLUR space with the D2P, the LD2P+, and with convex combinations of slices of arbitrary small diameter is also given.
Stability andl1-Gain Analysis for Positive 2D Systems with State Delays in the Roesser Model
2013
This paper considers the problem of delay-dependent stability andl1-gain analysis for positive 2D systems with state delays described by the Roesser model. Firstly, the copositive-type Lyapunov function method is used to establish the sufficient conditions for the addressed positive 2D system to be asymptotically stable. Then,l1-gain performance for the system is also analyzed. All the obtained results are formulated in the form of linear matrix inequalities (LMIs) which are computationally tractable. Finally, an illustrative example is given to verify the effectiveness of the proposed results.
Filtering for Discrete Fuzzy Stochastic Time-Delay Systems with Sensor Saturation
2013
Published version of an article from the journal: Mathematical Problems in Engineering. Also available from Hindawi: http://dx.doi.org/10.1155/2013/146325 This paper addresses the H-infinity filtering problem for discrete fuzzy stochastic systems with time-varying delay and sensor saturation. Random noise depending on state and external disturbance is also taken into account. A decomposition approach is employed to solve the characteristic of sensor saturation. The scaled small gain (SSG) theorem is extended to the stochastic systems, which is employed to handle with the time-varying delay by transforming the original system into the form of an interconnected system consisting of two subsys…
Compression of binary images based on covering
1995
The paper describes a new technique to compress binary images based on an image covering algorithm. The idea is that binary images can be always covered by rectangles, univocally described by a vertex and two adjacent edges (L-shape). Some optimisations are necessary to consider degenerate configurations. The method has been tested on several images representing drawings and typed texts. The comparison with existing image file compression techniques shows a good performance of our approach. Further optimisations are under development.
A Modified Tabu Thresholding Approach for the Generalised Restricted Vertex Colouring Problem
1996
We present a modification of the Tabu Thresholding (TT) approach and apply it to the solution of the generalised restricted vertex colouring problem. Both the bounded and unbounded cases are treated. In our algorithms, the basic TT elements are supplemented with an evaluation function that depends on the best solution obtained so far, together with a mechanism which reinforces the aggressive search in the improving phase, and new diversification strategies which depend on the state of the search. The procedure is illustrated through the solution of the problem of minimising the number of workers in a heterogeneous workforce.
Electronic transport in molecular junctions : The generalized Kadanoff–Baym ansatz with initial contact and correlations
2021
The generalized Kadanoff-Baym ansatz (GKBA) offers a computationally inexpensive approach to simulate out-of-equilibrium quantum systems within the framework of nonequilibrium Green's functions. For finite systems the limitation of neglecting initial correlations in the conventional GKBA approach has recently been overcome [Phys. Rev. B 98, 115148 (2018)]. However, in the context of quantum transport the contacted nature of the initial state, i.e., a junction connected to bulk leads, requires a further extension of the GKBA approach. In this work, we lay down a GKBA scheme which includes initial correlations in a partition-free setting. In practice, this means that the equilibration of the …