G-invariant norms and bicircular projections
نویسندگان
چکیده
It is shown that for many finite dimensional normed vector spaces V over C, a linear projection P : V → V will have nice structure if P + λ(I − P ) is an isometry for some complex unit not equal to one. From these results, one can readily determine the structure of bicircular projections, i.e., those linear projections P such that P + μ(I − P ) is a an isometry for every complex unit μ. The key ingredient in the proofs is the knowledge of the isometry group of the given norm. The proof techniques also apply to real vector spaces. In such cases, characterizations are given to linear projections P such that P−(I−P ) = 2P−I is an isometry. Mathematics Subject Classification (2000). Primary 15A60, 46B04.
منابع مشابه
Primitive Ideal Space of Ultragraph $C^*$-algebras
In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$ associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $ C^* $-algebra $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...
متن کاملOn the number of bases of bicircular matroids
Let t(G) be the number of spanning trees of a connected graph G, and let b(G) be the number of bases of the bicircular matroid B(G). In this paper we obtain bounds relating b(G) and t(G), and study in detail the case where G is a complete graph Kn or a complete bipartite graph Kn,m.
متن کاملRepresentations of bicircular matroids
Coullard, C.R., J.G. de1 Greco and D.K. Wagner, Representations of bicircular matroids, Discrete Applied Mathematics 32 (1991) 223-240. A bicircular matroid is a matroid defined on the edge set of a graph. Two different graphs can have the same bicircular matroid. The first result of this paper is a characterization of the collection of graphs having the same bicircular matroid as a given arbit...
متن کاملBicircular matroids representable over GF(4) or GF(5)
Given a bicircular matroid B(G) and q ∈ {4, 5}, we characterize when the bicircular matroid B(G) is GF (q)-representable by precisely describing the structure of G. These descriptions yield polynomial-time algorithms with input G to certify if B(G) is or is not GF (q)-representable.
متن کاملEmergence of Phase- and Shift-Invariant Features by Decomposition of Natural Images into Independent Feature Subspaces
Olshausen and Field (1996) applied the principle of independence maximization by sparse coding to extract features from natural images. This leads to the emergence of oriented linear filters that have simultaneous localization in space and in frequency, thus resembling Gabor functions and simple cell receptive fields. In this article, we show that the same principle of independence maximization...
متن کامل