Existence of optimal transport maps in very strict $$CD(K,\infty )$$ -spaces

We introduce a more restrictive version of the strict \(CD(K,\infty )\) -condition, the so-called very strict \(CD(K,\infty )\) -condition, and show the existence of optimal maps in very strict \(CD(K,\infty )\) -spaces despite the possible lack of uniqueness of optimal plans.     

A remark on CD 0(K)-spaces

A representation of the CD ₀(K)-space is given in [1, 2] for a compact Hausdorff space K without isolated points. We generalize this to an arbitrary countably compact space K without any assumption on isolated points.     

Linearization of holomorphic mappings onC(K)-spaces

We prove a universal mapping theorem for “integral” holomorphic mappings on the open unit ball ofC(K). In our theorem, the universal space isC(K), and the universal mapping is increasing in the positive cone ofC(K).     

(a)-spaces and selectively (a)-spaces from almost disjoint families

We investigate a selective version of property (a) and prove a number of results showing that, under certain set theoretical conditions, (a) spaces and selectively (a) spaces behave in a very similar way, at least for separable spaces. Several results regarding the presence of the referred selective version in spaces from almost disjoint families are established; in particular, we give a combinatorial characterization of such presence. Consistent set theoretical hypotheses implying equivalence between being (a) and being selectively (a) within the referred class are presented, as well as hypotheses implying non-equivalence. We also show that the Continuum Hypothesis is independent of the statement asserting the above mentioned equivalence. The paper finishes by presenting some notes and questions on the role of set theoretical assumptions in the subject.     

The Banach method and the monotone mapping method for finding optimal controls in reflexive (B)-spaces

Control and observation problems for operator equations of the first kind in reflexive strictly convex Banach spaces are considered. A BUME (Banach uniqueness and existence) method and a method of monotone nonlinear mappings for finding optimal (i.e., norm-minimal) controls are proposed, and an abstract maximum principle is stated. Under the additional assumption of separability and smoothness on (B)-spaces, an optimal control is found by the Galerkin method. As applications, ODE systems and partial differential equations are considered.     

Hyperbolic spaces,principal series,and $${\mathrm{O}}(2,\infty )$$O(2,∞)

We prove that there exists no irreducible representation of the identity component of the isometry group $${\mathrm{PO}}(1,n)$$ of the real hyperbolic space of dimension n into the group $${\mathrm{O}}(2,\infty )$$ if $$n\ge 3$$. This is motivated by the existence of irreducible representations (arising from the spherical principal series) of $${\mathrm{PO}}(1,n)^{\circ }$$ into the groups $${\mathrm{O}}(p,\infty )$$ for other values of p.     

The property (MLUR) in symmetric (KB)-spaces

Translated from Matematicheskie Zametki, Vol. 52, No. 6, pp. 149–151, December, 1992.     

Remarks on regular (LF)-spaces

Developing ideas found in a recent paper of Gilsdorf to arbitrary topological vector spaces (tvs) one shows that a Hausdorff (LB) _tv -spaceE is regular provided every null-sequence inE has a series convergent subsequence inE. Received by the editors 1980Mathematics Subject Classification (1985 Revision) 46A12.     

An inequality between thep- and (p, 1)-summing norm of finite rank operators fromC(K)-spaces

We show, for any operatorT from aC(K)-space into a Banach space with rank (T)≤n, the inequality , whereC≤4.671 is a numerical constant. The factor (1+logn)^1−1/p is asymptotically correct. This inequality extends a result of Jameson top ≠ 2. Several applications are given — one is a positive solution of a conjecture of Rosenthal and Szarek: For 1≤p<q<2,      

L^2[a,\infty)上高阶 Sturm-Liouville 算子下半有界性与谱

采用泛函分析与不等式渐近估计的方法,根据微分算子系数的特点,研究了高阶Sturm-Liouville微分算子下半有界性并得到其为下半有界的一些判定准则,同时给出了其下界的估计.这些结果对研究微分算子的谱是有益的.     

Algebras of holomorphic mappings in (DF)-spaces

Let U be an absolutely convex open subset of a complex barrelled (DF)-space E and let F be a commutative Banach algebra with identity. Let H_b(U, F) be the space of holomorphic mappings from U into F that are bounded on the U-bounded sets and let H_b (U, F) be the space of the holomorphic mappings from U into F that are uniformly weakly continuous on the U-bounded sets, both endowed with the topology τ_b of uniform convergence on the U-bounded sets. The spectra of (H_wu (U, F), τ_b) and (H_b(U, F), τ_b) are studied.     

On extension of isometries in (F)-spaces

An (F)-spaceE is said to be locally midpoint constricted (in short, Imp-constricted) if there exists some>0 such thatD(A/2) <D(A) for every subsetA ofE with 0<D(A), whereD(A) denotes the diameter ofA. Our main result goes as follow: LetE be an Imp-constricted (F)-space andU an open connected subset ofE. Assume thatT:U F is an isometry (i.e., a distance-preserving map) which mapsU onto an open subset of the (F)-spaceF. ThenT can be extended to an affine homeomorphism fromE toF. Also, some other results about the question whether each isometry between two (F)-spaces is affine are obtained.     

Weighted (LF)-spaces of Continuous Functions

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