We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. W...

Let L be a positive line bundle over a projective complex manifold X , L its tensor power of order p, H(X,L) the space of holomorphic sections of L and Np the complex dimension of H(X,L). The determinant of a basis ofH(X,L), together with some given probability measure on a weighted compact set in X , induces naturally a βensemble, i.e., a random Np-point process on the compact set. Physically,...

In [l], we proved a criterion for the disjointness of two induced representations UL and UM of a Lie group G, where L and M are finite-dimensional unitary representations of compact subgroups H and R, respectively, of G. The purpose of this paper is to improve this theorem by getting a stronger conclusion, while dropping the conditions that G be a Lie group and H be compact, and that L and M he...

dL(Mo,M1) = inf[llogdil/l + Ilogdil/-II], f where I: Mo -+ MI is a homeomorphism and dil I is the dilatation of I given by dill = SUPXt#2 dist(f(x l ), l(x2))/ dist(x1 ,x2). If Mo and MI are not homeomorphic, define dL(Mo,M1) = +00. Gromov [20] proves the remarkable result that the space of compact Riemannian manifolds L(A,t5 ,D) of sectional curvature IKI :::; A, injectivity radius i M 2: t5 >...

By a theorem of Andreotti and Grauert if ω is a (p, q) current, q < n, in a Stein manifold, ∂̄ closed and with compact support, then there is a solution u to ∂̄u = ω still with compact support. The main result of this work is to show that if moreover ω ∈ L(dm), where m is a suitable Lebesgue measure on the Stein manifold, then we have a solution u with compact support and in L(dm). We prove it by...

Let L be a non empty reflexive relational structure. The functor CompactSublatt(L) yields a strict full relational substructure of L and is defined as follows: (Def. 1) For every element x of L holds x ∈ the carrier of CompactSublatt(L) iff x is compact. Let L be a lower-bounded non empty reflexive antisymmetric relational structure. Observe that CompactSublatt(L) is non empty. Next we state th...

In this article the frame-theoretic account of what is archimedean for order-algebraists, and semisimple for people who study commutative rings, deepens with the introduction of J -frames: compact normal frames that are join-generated by their saturated elements. Yosida frames are examples of these. In the category of J -frames with suitable skeletal morphisms, the strongly projectable frames a...

This paper develops several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift-invariant subspaces of L 2 (G) in terms of range functions. Utilizing these functions, we generalize characterizations of frames and Ries...

Let L be the space of line transversals to a nite family of pairwise disjoint compact convex sets in R 3. We prove that each connected component of L can itself be represented as the space of transversals to some nite family of pairwise disjoint compact convex sets.

We show that sequences of compact gradient Ricci solitons converge to complete orbifold gradient solitons, assuming constraints on volume, the L-norm of curvature, and the auxiliary constant C1. The strongest results are in dimension 4, where L 2 curvature bounds are equivalent to upper bounds on the Euler number. We obtain necessary and sufficient conditions for limits to be compact.