相关论文: Two remarks on the interpolation space

If $U$ is a unitary operator on a separable complex Hilbert space $\mathcal{H}$, an application of the spectral theorem says there is a conjugation $C$ on $\mathcal{H}$ (an antilinear, involutive, isometry on $\mathcal{H}$) for which $ C U…

We give a characterization of onto interpolating sequences with finite associated measure for the Dirichlet space in terms of condenser capacity. In the Sobolev space $H_1(\mathbb{D})$ we define a natural notion of onto interpolation and we…

The monograph contains the detailed exposition of the results obtained by the author during the last several years. In particular it contains an improvement of the well known Calderon - Ryff interpolation theorem and description of…

In this mostly expository article, we provide a new account of our proof with Minsky and Sisto that mapping class groups and Teichm\"uller spaces admit bicombings. More generally, we explain how the hierarchical hull of a pair of points in…

This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…

We prove that the isomorphism relation for separable C$^*$-algebras, and also the relations of complete and $n$-isometry for operator spaces and systems, are Borel reducible to the orbit equivalence relation of a Polish group action on a…

We study the space of all $d$-tuples of unitaries $u=(u_1,\ldots, u_d)$ using dilation theory and matrix ranges. Given two $d$-tuples $u$ and $v$ generating C*-algebras $\mathcal A$ and $\mathcal B$, we seek the minimal dilation constant…

We study the interpolation and extrapolation properties of strictly singular operators between different $L_p$ spaces. To this end, the structure of strictly singular non-compact operators between $L_p-L_q$ spaces is analyzed. Among other…

In \cite{Craig}, we introduced a syntactically defined and highly general class of calculi known as \emph{semi-analytic}. We then demonstrated that any sufficiently strong (modal) substructural logic with a semi-analytic calculus must…

We consider two inclusions of $C^*$-algebras whose small $C^*$-algebras have approximate units of the large $C^*$-algebras and their two spaces of all bounded bimodule linear maps. We suppose that the two inclusions of $C^*$-algebras are…

On any complete Riemannian manifold $M$ and for all $p\in [2,\infty)$, we prove a family of second order $L^{p}$-interpolation inequalities that arise from the following simple $L^{p}$-estimate valid for every $u \in C^{\infty}(M)$: $$…

Let $M^n\ (n\geq3)$ be a complete Riemannian manifold with $\sec_M\geq 1$, and let $M_i^{n_i}$ ($i=1,2$) be two comlplete totally geodesic submanifolds in $M$. We prove that if $n_1+n_2=n-2$ and if the distance $|M_1M_2|\geq\frac{\pi}{2}$,…

An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities…

Measure homology is a variation of singular homology designed by Thurston in his discussion of simplicial volume. Zastrow and Hansen showed independently that singular homology (with real coefficients) and measure homology coincide…

The closed one-sided ideals of a C*-algebra are exactly the closed subspaces supported by the orthogonal complement of a closed projection. Let A be a (not necessarily selfadjoint) subalgebra of a unital C*-algebra B which contains the unit…

We consider the $O(3)$ nonlinear sigma model with the $\theta$-term and its linear counterpart in 1+1D. The model has discrete time-reflection and space-reflection symmetries at any $\theta$, and enjoys the periodicity in $\theta\rightarrow…

The homology with coefficients in a field of the configuration spaces $C(M\times \bold R ^n,M_o\times \bold R ^n;X)$ is determined in this paper.

We prove that for $1\le p,q\le\infty$ the mixed-norm spaces $L_q(L_p)$ are mutually non-isomorphic, with the only exception that $L_q(L_2)$ is isomorphic to $L_q(L_q)$ for all $1<q<\infty$.

Normal modal logics extending the logic K4.3 of linear transitive frames are known to lack the Craig interpolation property, except some logics of bounded depth such as S5. We turn this `negative' fact into a research question and pursue a…

For any $\theta>\frac13$, we show that there are constants $c_1,c_2>0$ that depend only on $\theta$ for which the following property holds. If $\chi_1,\chi_2$ are two distinct primitive Dirichlet characters modulo $q$, and $T\ge…