Grothendieck spaces: the landscape and perspectives
نویسندگان
چکیده
In 1973, Diestel published his seminal paper Grothendieck spaces and vector measures that drew a connection between (Banach for which weak- weak*-sequential convergences in the dual space coincide) measures. This was developed further book with J. Uhl Jr. Vector Additionally, Diestel’s included section several open problems about structural properties of spaces, only half them have been solved to this day. The present aims at synthetically presenting state art subjectively selected corners theory Banach property, describing main examples recording solutions problems, providing generalisations/extensions or new proofs various results concerning adding list we believe are relevance may reinvigorate better-structured development theory.
منابع مشابه
Grothendieck fibrations and classifying spaces
Grothendieck fibrations have played an important role in homotopy theory. Among others, theywereused byThomason to describehomotopy colimits of small categories and byQuillen to derive long exact sequences of higher K-theory groups. We construct simplicial objects, namely the fibred and the cleaved nerve, to characterize the homotopy type of a Grothendieck fibration by using the additional stru...
متن کاملTeichmüller spaces, triangle groups and Grothendieck dessins
This survey article considers moduli of algebraic curves using techniques from the complex analytic Teichmüller theory of deformations for the underlying Riemann surfaces and combinatorial topology of surfaces. The aim is to provide a readable narrative, suitable for people with a little background in complex analysis, hyperbolic plane geometry and discrete groups, who wish to understand the in...
متن کاملHolonomy Quantization of Moduli Spaces & Grothendieck Groups
Gelfand’s [1] charecterization of a topological space M by the duality relationship of M and A = F(M), the commutative algebra of functions on this space has deep implications including the development of spectral calculas by Connes [2].We investigate this scheme in this paper in the context of Monopole Moduli Space M using Seiberg-Witten Equations [3].A observation has been made here that the ...
متن کاملQuasinormable Spaces and the Problem of Topologies of Grothendieck
This article is dedicated to the study of quasinormable injective tensor products of locally convex spaces and quasinormable spaces of continuous linear operators. The stability of the quasinormability is obtained in the frame of the class of spaces which are quasinormable by operators; this class, introduced and studied here, contains many function spaces. The problems considered in the articl...
متن کاملThe Algebras of Bounded Operators on the Tsirelson and Baernstein Spaces Are Not Grothendieck Spaces
We present two new examples of re exive Banach spaces X for which the associated Banach algebra B(X) of bounded operators on X is not a Grothendieck space, namelyX = T (the Tsirelson space) andX = Bp (the p th Baernstein space) for 1 < p <∞.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Japanese journal of mathematics
سال: 2021
ISSN: ['0289-2316', '1861-3624']
DOI: https://doi.org/10.1007/s11537-021-2116-3