Entropy quantities are connected with the 'degree of compactness' of compact or precompact spaces, and so are appropriate tools for investigating linear and compact operators between Banach spaces. The main intention of this Tract is to study the relations between compactness and other analytical properties, e.g. approximability and eigenvalue sequences, of such operators. The authors present many generalized results, some of which have not appeared in the literature before. In the final chapter, the authors demonstrate that, to a certain extent, the geometry of Banach spaces can also be developed on the basis of operator theory. All mathematicians working in functional analysis and operator theory will welcome this work as a reference or for advanced graduate courses.

No abstract

The paper gives i t characterization of right-hand quotients d = Al o -4;' of surjective operat,or ideals A, iiiid 112 which refers to so cnlled "generitting systems of sets". Siinultmeously the corresponding "inversion formulas" Basic concepts and notationsThe present paper deals with a special method for geneiating o p n t o r ideals o ?~ the class of all UANACH spaces. The general riotion of an operator ideal can he looked np in [lo] and in various research papers.The teriii "operator" refer? to a eontinuous linear map froiii a BANACH space I.J into a BANACH space F . The class of all these iiiaps is denoted by L(E, F ) . The notation A ( E , F ) concerns the class of operators T E L(E, F ) belorigiiig to a given operator ideal A .The rig?![-hand quotient A, o A;, of two operator ideals A, rmcl A, is defined to lw the class of operators T such that T S belongs to A, for all X of type A,. Similarly the left-htrnd yuotzejit o A, is meant to he the class of operators T such that AST 1s of type 9, for all S of type A,. Finally the ptoduct A, o A, of two opercctor ideuls A, and A, qtaiids for the class of operators T which can be represented by a product T = BS, \$liere R is of type A, and S of type A,. Quotients and products of operator ideal? again turn out to he operator ideals (cf. [lo], [HI).The notion of r( surjectave opetator ideutl, which is basic for this paper, has hcc.11 introduced in [14] and [15]. Roughly speaking, surjectivity of an operator ideal ,1 tiieans that the operators 7' E A ( K , F ) are characterized by the nature of the image 7'(UE) they iiiake from the unit hall UE of the BANACH space E'. Indeed, denoting the closed unit balls of any BANACH spaces E and E , hy U, and UEo, respectively, e ('itii descrihe a u r p t iziity of u 71 operutor deal A as follows :An cyiiivalent cliaracterizatioii of surjectivity says that Given HI^ arhit.mry opcrator idcal A the .wrjective hull As is meant to he the crlnss of operator# 7' which ace siibject to an inclusion

No abstract

No abstract