Genericity and Universality for Operator Ideals

A bounded linear operator $U$ between Banach spaces is universal for the complement of some operator ideal $\mathfrak{J}$ if it is a member of the complement and it factors through every element of the complement of $\mathfrak{J}$. In the first part of this paper, we produce new universal operators for the complements of several ideals, and give examples of ideals whose complements do not admit such operators. In the second part of the paper, we use descriptive set theory to study operator ideals. After restricting attention to operators between separable Banach spaces, we call an operator ideal $\mathfrak{J}$ generic if whenever an operator $A$ has the property that every operator in $\mathfrak{J}$ factors through a restriction of $A$, then every operator between separable Banach spaces factors through a restriction of $A$. We prove that many classical operator ideals (such as strictly singular, weakly compact, Banach–Saks) are generic and give a sufficient condition, based on the complexity of the ideal, for when the complement does not admit a universal operator. Another result is a new proof of a theorem of M. Girardi and W. B. Johnson, which states that there is no universal operator for the complement of the ideal of completely continuous operators.

RNPLS&T’s e-library: The history, development dynamics, technologies, and resources

The history of RNPLS&T E-library and Electronic Archive of heterogeneous information resource since 2006 is discussed. Development of RNPLS&T’s in-house digital resources is also examined. Special attention is given to the E-library development dynamics in 2011–2018. The most popular thematic collections for 2017 are analyzed. The Electronic Archive technological platform for digitized documents processing, hosting, storing and presenting is discussed in detail. The authors argue that with implementing the Electronic Archive the efficiency of digital books generation increased due to universal operator interface, which enables to prepare and host digital documents on several workstations. The technology of incoming documents processing for RNPLS&T’s E-library is based on the IRBIS64 LAS technologies and RNPLS&T’s E-catalog and enables to extract entries generated within a given time period. The technology specific feature is that in every extracted bibliographic record, digitized resource URL is changed to PURL (Persistent URL), which enables to relocate, if necessary, the digitized documents to another depository without changing its bibliographic description.The relevance of user demanded documents from the RNPLS&T’s E-library is analyzed.The authors acknowledge that RNPLS&T’s E-library resources in engineering make a significant part of the digital resources of the National Electronic Library.