A weak∗-topological dichotomy with applications in operator theory

A weak∗-topological dichotomy with applications in operator theory

Denote by [0, ω1) the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let C0[0, ω1) be the Banach space of scalar-valued, continuous functions which are defined on [0, ω1) and vanish eventually. We show that a weak ∗compact subset of the dual space of C0[0, ω1) is either uniformly Eberlein compact, or it contains a homeomorphic copy of...

Topological Sectors and a Dichotomy in Conformal Field Theory

Let A be a local conformal net of factors on S1 with the split property. We provide a topological construction of soliton representations of the n-fold tensor product A⊗ · · · ⊗ A, that restrict to true representations of the cyclic orbifold (A ⊗ · · · ⊗ A)Zn . We prove a quantum index theorem for our sectors relating the Jones index to a topological degree. Then A is not completely rational if...

Weak hyper semi-quantales and weak hypervalued topological spaces

The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...

Operator theory and its applications

A Dichotomy on Constrained Topological Sorting

We introduce the constrained topological sorting problem (CTS-problem): given a target language L and a directed acyclic graph (DAG) G with labeled vertices, determine if G has a topological sort which forms a word that belongs to L. This natural problem applies to several settings, including scheduling with costs or verifying concurrent programs. It also generalizes the shuffle problem of form...