The Catholic Calumet

Property $ \bf{(wL)}$ and the reciprocal Dunford-Pettis property in projective tensor products

“…Hence {T * n y * * : n ∈ N} is an L-subset of X * . Therefore this subset is relatively weakly compact [27]. This verifies (ii) of Theorem 1.…”

“…and let (T n ) be a sequence in H. The proof of Theorem 6 shows that {T n x : n ∈ N} is an L-subset of Y * , and thus relatively weakly compact by [27]. Similarly, {T * n y * * : n ∈ N} is an L-subset of X * , thus relatively weakly compact.…”

“…The unit ball of X will be denoted by B X , and XThe Banach space X has the reciprocal Dunford-Pettis property (RDP P ) if every completely continuous operator T from X to any Banach space Y is weakly compact [25, p. 153]. The space X has the RDP P if and only if every L-subset of X * is relatively weakly compact [27]. Banach spaces with property (V ) of Pe lczyński, in particular reflexive spaces and C(K) spaces, have the RDP P [30].…”

The p-Gelfand–Phillips property in spaces of operators and Dunford–Pettis like sets

“…The Banach space X has the reciprocal Dunford-Pettis (RDP ) property if every completely continuous operator T from X to any Banach space Y is weakly compact [22, p. 153]. The space X has the RDP property if and only if every L-subset of X * is relatively weakly compact [23], [19]. Banach spaces with property (V ) of Pe lczyński, in particular reflexive spaces and C(K) spaces, have the RDP property [25].…”

The Reformation in Global Perspective

“…8 Tracy Neal Leavelle in his study of Jesuits in colonial North America summarized this perspective nicely as the "adoption of a plural, dynamic, and f lexible concept of conversion that accounts for the changes in all participants." 9 In part, the slipperiness of conversion stemmed from the protracted debates among missionaries over the boundaries of accommodation with local practices in Mexico, China, India, Africa, and Europe. Yet differences over the degree of acceptable accommodation coincided with the distinct cultural meanings indigenous peoples attached to the messages they absorbed.…”