We introduce the concept of reflexivity for bounded n-linear maps and investigate the reflexivity of Zn(L1(G),X), the space of bounded ncocycles from L1(G)(n) into X, where L1(G) is the group algebra of a locally compact group G and X is a Banach L1(G)-bimodule. We show that Zn(L1(G), X) is reflexive for a large class of groups including groups with polynomial growth, IN-groups, maximally almos...

The main result is that a Banach space X is not super-reflexive if and only if the diamond graphs Dn Lipschitz embed into X with distortions independent of n. One of the consequences of that and previously known results is that dimension reduction a-la Johnson–Lindenstrauss fails in any non super reflexive space with non trivial type. We also introduce the concept of Lipschitz (p, r)-summing ma...

1. As in [l], 51 will denote a space of points P with a countably additive, non-negative measure y(E); all sets and functions considered will be 7-measurable; e will always denote a set of finite measure; E will be called purely infinite if y(E) = <» and eC-E implies y(e) =0. X is a length function if \(m) is defined, with O^X(m) fk °° , for every non-negative function u=u(P), and satisfies: (L...

AIM This paper is a report of a discussion of the arguments surrounding the role of the initial literature review in grounded theory. BACKGROUND Researchers new to grounded theory may find themselves confused about the literature review, something we ourselves experienced, pointing to the need for clarity about use of the literature in grounded theory to help guide others about to embark on s...

Let T be a bounded operator on the Hilbert space Jf. We denote by W{T) the weakly closed algebra generated by T and / and, as usual, we denote by Alg Lat(T') the set of those operators X with the property that XM c M whenever M is an invariant subspace for T. Of course, we always have W{T) <= Alg Lat(r), and T is said to be reflexive if W{T) = Alg Lat(7). The letter S will always stand for the ...

Uncertainty in digital service ecosystems (DSEs) can be attributed to several factors like the dynamic nature of the ecosystem and unknown deployment environment, change and evolution of requirements, and co-evolution among ecosystem members. Managing uncertainties in DSEs is challenging, and therefore, novel and solid software architecting methods, techniques and tools are needed. Our research...

Proofs of equalities may be built from assumptions using proof rules for reflexivity, symmetry, and transitivity. Reflexivity is an axiom proving x=x for any x; symmetry is a 1-premise rule taking a proof of x=y and returning a proof of y=x; and transitivity is a 2-premise rule taking proofs of x=y and y=z, and returning a proof of x=z. Define an equivalence relation to hold between proofs iff ...

Reflexivity is actually a key term in the dramatic and rapid changes confronted by the human sciences (especially sociology) during the last four decades and “yet the word is used in so many different senses that it often sustains confusion rather than clarifying any underlying issues” (Holland, 1999: 463). In general, reflexivity was comprehensively defined by George Herbert Mead as “the turni...

Alongside other methodological affinities between contemporary Scandinavian information systems research and social anthropology, the modes of reflexivity that have come to characterize each differ. Reflexivity in the former concerns an ‘otherness’ of technology, which is related to the users and their practices, while reflexivity within social anthropology concerns the encounter between the te...