New perturbation theorems are proved for simultaneous bases of singular subspaces of real matrices. These results improve the absolute bounds previously obtained in [6] for general (complex) matrices. Unlike previous results, which are valid only for the Frobenius norm, the new bounds, as well as those in [6] for complex matrices, are extended to any unitarily invariant matrix norm. The bounds ...

In this paper we continue the study of central subspaces initiated in [2] and its infinite version called almost constrained subspaces. We are interested in studying situations where these intersection properties of balls lead to the existence of a linear projection of norm one. We show that every finite dimensional subspace is a central subspace only in Hilbert spaces. By considering direct su...

For a complete measure space (X,Σ,μ), we give conditions which force Lp(X,μ), for 1 ≤ p < ∞, to be isometrically isomorphic to p(Γ) for some index set Γ which depends only on (X,μ). Also, we give some new characterizations which yield the inclusion Lp(X,μ)⊂ Lq(X,μ) for 0<p < q.

Some simplifications of Schaffer's girth and perimeter of the unit spheres are introduced. Their general properties are discussed, and they are used to study the lp, Lp spaces, uniformly nonsquare spaces, and their isomorphic classes. 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 46 B 20.

G. BIRKHOFF and J . v . NEUMANN1 have shown in 1936 that the closed linear manifolds (subspaces) of the Hilbert space form a complete atomic and ortho-complemented lattice LQ which at least for finite dimensional subspaces is also modular. JAUCH 2 ' 3 , PIRON4 and KAMBER5 have pointed out, that instead of the modularity a weeker condition can be formulated in LQ which is always fulfilled for th...

We present an integer linear program (IP), for the Graph Isomorphism (GI) problem, which has non-empty feasible solution if and only if the input pair of graphs are isomorphic. We study the polytope of the convex hull of the solution points of IP, denoted by B. Exponentially many facets of this polytope are known. We show that in case of non-isomorphic pairs of graphs if a feasible solution exi...

Let Γ = (P,L) be a parapolar space which is locally An−1,3(K) for some integer n > 6 and K a field. There exists a class of 2-convex subspaces D, each isomorphic to D5,5(K), such that every symplecton of Γ is contained in a unique element of D. Let Γ = (P,L) be a parapolar space which is locally An−1,4(K) for n = 7 or an integer n ≥ 9 and some field K. Assume that Γ satisfies the extra conditio...

We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing distance inequalities. also a sharp upper estimate outer volume ratio from an arbitrary convex body unit balls subspaces $L_p$.