In this paper, two outwardly different graphs, namely, the zero-divisor graph [Formula: see text] and comaximal of ring all real-valued continuous functions having countable range, defined on any zero-dimensional space text], are investigated. It is observed that these graphs exhibit resemblance, so far as diameters, girths, connectedness, triangulatedness or hypertriangulatedness concerned. Ho...

We show that there are no automorphic Banach spaces of the form C(K) with K continuous image of Valdivia compact except the spaces c0(Γ). Nevertheless, when K is an Eberlein compact of finite height such that C(K) is not isomorphic to c0(Γ), all isomorphism between subspaces of C(K) of size less than אω extend to automorphisms of C(K).

We construct a complete metric space M of cardinality continuum such that every non-singleton closed separable subset fails to be Lipschitz retract M. This provides analogue the various classical and recent examples Banach spaces failing have linearly complemented subspaces prescribed smaller density character.

Similarity search has been widely used in many applications such as information retrieval, image data analysis, and time-series matching. Specifically, a similarity query retrieves all data objects in a data set that are similar to a given query object. Previous work on similarity search usually consider the search problem in the full space. In this paper, however, we propose a novel problem, s...

We investigate properties of subspaces of L2 spanned by subsets of a finite orthonormal system bounded in the L∞ norm. We first prove that there exists an arbitrarily large subset of this orthonormal system on which the L1 and the L2 norms are close, up to a logarithmic factor. Considering for example the Walsh system, we deduce the existence of two orthogonal subspaces of L2 , complementary to...

3. Since Lp and Lr are subspaces of CX , their intersection is a vector space. It is clear that ‖ · ‖ is a norm (this follows directly from the fact that ‖ · ‖p and ‖ · ‖r are norms). Let 〈fn〉n=1 be a Cauchy sequence in Lp ∩ Lr. Since ‖fm − fn‖p ≤ ‖fm − fn‖ and ‖fm − fn‖r ≤ ‖fm − fn‖ for all m,n ∈ N, it is clear that 〈fn〉n=1 is a Cauchy sequence in both Lp and Lr. Let gp ∈ Lp and gr ∈ Lr be the...

Enflo and Rosenthal [4] proved that `p(א1), 1 < p < 2, does not (isomorphically) embed into Lp(μ) with μ a finite measure. We prove that if X is a subspace of an Lp space, 1 < p < 2, and `p(א1) does not embed into X, then X embeds into Lp(μ) for some finite measure μ.

We prove almost sharp upper bounds for the Lp norms of eigenfunctions of the full ring of invariant differential operators on a compact locally symmetric space, as well as their restrictions to maximal flat subspaces. Our proof combines techniques from semiclassical analysis with harmonic theory on reductive groups, and makes use of new asymptotic bounds for spherical functions that are of inde...

in this paper, we show that in each nite dimensional hilbert space, a frame of subspaces is an ultra bessel sequence of subspaces. we also show that every frame of subspaces in a nite dimensional hilbert space has frameness bound.

In this paper we study the structure of the Banach space K(E, F) of all compact linear operators between two Banach spaces E and F. We study three distinct problems: weak compactness in K(E, F), subspaces isomorphic to l~ and complementation of K(E, F) in L(E, F), the space of bounded linear operators. In § 2 we derive a simple characterization of the weakly compact subsets of K(E, F) using a c...