Related papers: The classification problem for finitely generated …
We conjecture that satellite operations are either constant or have infinite rank in the concordance group. We reduce this to the difficult case of winding number zero satellites, and use $SO(3)$ gauge theory to provide a general criterion…
We prove that the set of all complex symmetric operators on a separable, infinite-dimensional Hilbert space is not norm closed.
A finite-dimensional complex space with indefinite scalar product [.,.] having v- = 2 negative squares and v+ >= 2 positive ones is considered. The paper presents a classification of operators that are normal with respect to this product.…
Finite-dimensional model spaces are quotient spaces of the Hardy space on the open unit disc, determined by finite Blaschke products. Composition operators, on the other hand, act by composing Hardy space functions with analytic self-maps…
We investigate $\mathcal F$-Borel topological spaces. We focus on finding out how a~complexity of a~space depends on where the~space is embedded. Of a~particular interest is the~problem of determining whether a~complexity of given space $X$…
A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…
We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product is separable or entangled. We show that the tensor convolution defined for certain mappings on an almost arbitrary…
We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply defined compact spaces,…
Generally-unbounded infinitesimal generators are studied in the context of operator topology. Beginning with the definition of seminorm, the concept of locally convex topological vector space is introduced as well as the concept of…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…
For $1<p\leqslant \infty$, we study the complexity and the existence of universal spaces for two classes of separable Banach spaces, denoted $\textsf{A}_p$ and $\textsf{N}_p$, and related to asymptotic smoothness in Banach spaces. We show…
We classify order $3$ linear difference operators over $\mathbb{C}(x)$ that are solvable in terms of lower order difference operators. To prove this result, we introduce the notion of absolute irreducibility for difference modules, and…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We prove that it is not possible to classify separable von Neumann factors of types $\II_1$, $\II_\infty$ or $\III_\lambda$, $0\leq \lambda\leq1$, up to isomorphism by a Borel measurable assignment of "countable structures" as invariants.…
The Paulsen Problem in Hilbert space frame theory has proved to be one of the most intractable problems in the field. We will help explain why by showing that this problem is equivalent to a fundamental, deep problem in operator theory.…
We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…
We first show that infinite satisfiability can be reduced to finite satisfiability for all prenex formulas of Separation Logic with $k\geq1$ selector fields ($\seplogk{k}$). Second, we show that this entails the decidability of the finite…
We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…
A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have…
We prove that the equivalence of pure states of a separable C*-algebra is either smooth or it continuously reduces $[0,1]^{\bbN}/\ell_2$ and it therefore cannot be classified by countable structures. The latter was independently proved by…