Related papers: Lipschitz tensor product

We investigate the first-order differential calculus over extended metric-topological measure spaces. The latter are quartets $\mathbb X=(X,\tau,{\sf d},\mathfrak m)$, given by an extended metric space $(X,{\sf d})$ together with a weaker…

We introduce and study a new Banach algebra structure on the trace-zero subspace $\mathcal{T}(L^2(\mathbb{G}))_0$ of trace class operators for any locally compact quantum group $\mathbb{G}$; it is defined through a mixed Lie-type product of…

Given two correspondences $X$ and $Y$ and a discrete group $G$ which acts on $X$ and coacts on $Y$, one can define a twisted tensor product $X\boxtimes Y$ which simultaneously generalizes ordinary tensor products and crossed products by…

Let $E, F, E_0$ be Banach spaces, with $E_0$ a subspace of $E$. For a maximal Banach operator ideal $\mathcal{A}$, we show that a linear operator from $E_0$ to $F$ can be extended to a linear operator from $E$ to $F$ that belongs to…

Let $m,n$ be positive integers with $m<n$. Under certain assumptions on the Banach space $X$, we prove that the $n$-fold projective tensor product of $X$, $\widehat{\otimes}^n_\pi X$, is not isomorphic to any subspace of any quotient of the…

We develop the theory of subproduct systems over the monoid $\mathbb{N}\times \mathbb{N}$, and the non-self-adjoint operator algebras associated with them. These are double sequences of Hilbert spaces $\{X(m,n)\}_{m,n=0}^\infty$ equipped…

A Banach space operator $T\in B(X)$ is left polaroid if for each $\lambda\in\hbox{iso}\sigma_a(T)$ there is an integer $d(\lambda)$ such that asc $(T-\lambda)=d(\lambda)<\infty$ and $(T-\lambda)^{d(\lambda)+1}X$ is closed; $T$ is finitely…

Let $L$ be a linear operator in $L^2({{\mathbb R}^n})$ and generate an analytic semigroup $\{e^{-tL}\}_{t\ge 0}$ with kernels satisfying an upper bound of Poisson type, whose decay is measured by $\theta(L)\in (0,\infty].$ Let $\omega$ on…

We set up a descriptive set-theoretic framework to study Lipschitz-free spaces and use the reduction argument of Bossard to prove several results. We prove two universality results: if a separable Banach space is isomorphically universal…

We prove that any correspondence (multi-function) mapping a metric space into a Banach space that satisfies a certain pointwise Lipschitz condition, always has a continuous selection that is pointwise Lipschitz on a dense set of its domain.…

Let $G$ and $H$ be unital associative algebras over a field $K$, such that $G$ satisfies the identity $[x_1, \dots, x_p] = 0$ for some integer $p \geq 3$ and $H$ satisfies the identities $[x_1, x_2, x_3] = 0$ and $[x_1, x_2] \cdots…

The main purpose of the paper is to prove the following results: Let $A$ be a locally finite metric space whose finite subsets admit uniformly bilipschitz embeddings into a Banach space $X$. Then $A$ admits a bilipschitz embedding into $X$.…

The Lipschitz extension modulus $e(M)$ of a metric space $M$ is the infimum over $L\ge 1$ such that for any Banach space $Z$ and any $C\subset M$, any 1-Lipschitz function $f:C\to Z$ can be extended to an $L$-Lipschitz function $F:M\to Z$.…

We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of $\mathcal{L}_{p}$-spaces. We use…

Given a Banach lattice $L,$ the space of lattice Lipschitz operators on $L$ has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is…

A 1972 duality conjecture due to Pietsch asserts that the entropy numbers of a compact operator acting between two Banach spaces and those of its adjoint are (in an appropriate sense) equivalent. This is equivalent to a dimension free…

Recently, in arXiv:2304.07149, a bridge was made between the very active area of spaces of Lipschitz real functions on a metric space and holomorphic functions on an open subset of a Banach space. This was done by introducing and studying…

We show that for real Banach spaces that are either separable or dual spaces, the Lipschitz numerical index coincides with the classical (linear) numerical index. This result provides partial evidence toward the question posed by Wang,…

Let $X$ be a Banach space and $\mathcal A$ be the Banach algebra $B(X)$ of bounded (i.e. continuous) linear transformations (to be called operators) on $X$ to itself. Let $\mathcal E$ be the set of idempotents in $\mathcal A$ and $\mathcal…

For two given symmetric sequence spaces $E$ and $F$ we study the $(E,F)$-multiplier space, that is the space all of matrices $M$ for which the Schur product $M\ast A$ maps $E$ into $F$ boundedly whenever $A$ does. We obtain several results…