Grand and small spaces based on the Calderón’s construction

Abstract

We propose two general methods for defining grand and small spaces based on Calderón’s construction and prove some fundamental properties of these spaces. In particular, we give a complete description of associative spaces to general grand and small spaces. Our description allows us to give an exact answer to the question posed in [25]. We give some examples illustrating our constructions for spaces constructed on sets of finite and infinite measure.