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Register a new userProperties of Kondratiev spaces
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In this paper, we investigate Kondratiev spaces on domains of polyhedral type. In particular, we will be concerned with necessary and sufficient conditions for continuous and compact embeddings, and in addition we shall deal with pointwise multiplication in these spaces.
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We obtain several new characterizations of ultrametric spaces in terms of roundness, generalized roundness, strict p-negative type, and p-polygonal equalities (p > 0). This allows new insight into the isometric embedding of ultrametric spaces into Euclidean spaces. We also consider roundness properties additive metric spaces which are not ultrametric.
In this paper, we study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis (e_k) is said to be subsequentially minimal if for every normalized block basis (x_k) of (e_k), there is a further block (y_k) of (x_k) such that (y_k) is equivalent to a subsequence of (e_k). Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal and connections with Bourgains ell^{1}-index are established. It is also shown that a large class of mixed Tsirelson spaces fails to be subsequentially minimal in a strong sense.
We study the dynamics of the group of isometries of $L_p$-spaces. In particular, we study the canonical actions of these groups on the space of $delta$-isometric embeddings of finite dimensional subspaces of $L_p(0,1)$ into itself, and we show that for $p eq 4,6,8,ldots$ they are $varepsilon$-transitive provided that $delta$ is small enough. We achieve this by extending the classical equimeasurability principle of Plotkin and Rudin. We define the central notion of a Fraisse Banach space which underlies these results and of which the known separable examples are the spaces $L_p(0,1)$, $p eq 4,6,8,ldots$ and the Gurarij space. We also give a proof of the Ramsey property of the classes ${ell_p^n}_n$, $p eq 2,infty$, viewing it as a multidimensional Borsuk-Ulam statement. We relate this to an arithmetic version of the Dual Ramsey Theorem of Graham and Rothschild as well as to the notion of a spreading vector of Matouv{s}ek and R{o}dl. Finally, we give a version of the Kechris-Pestov-Todorcevic correspondence that links the dynamics of the group of isometries of an approximately ultrahomogeneous space $X$ with a Ramsey property of the collection of finite dimensional subspaces of $X$.
In this paper, for a locally compact commutative hypergroup $K$ and for a pair $(Phi_1, Phi_2)$ of Young functions satisfying sequence condition, we give a necessary condition in terms of aperiodic elements of the center of $K,$ for the convolution $fast g$ to exist a.e., where $f$ and $g$ are arbitrary elements of Orlicz spaces $L^{Phi_1}(K)$ and $L^{Phi_2}(K)$, respectively. As an application, we present some equivalent conditions for compactness of a compactly generated locally compact abelian group. Moreover, we also characterize compact convolution operators from $L^1_w(K)$ into $L^Phi_w(K)$ for a weight $w$ on a locally compact hypergroup $K$.
A notion of resolvent set for an operator acting in a rigged Hilbert space $D subset Hsubset D^times$ is proposed. This set depends on a family of intermediate locally convex spaces living between $D$ and $D^times$, called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.
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