2011
DOI: 10.4134/jkms.2011.48.4.823
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CONTINUITY OF (Α,β)-Derivatio OF OPERATOR ALGEBRAS

Abstract: We investigate the continuity of (α, β)-derivations on B(X) or C * -algebras. We give some sufficient conditions on which (α, β)derivations on B(X) are continuous and show that each (α, β)-derivation from a unital C * -algebra into its a Banach module is continuous when α and β are continuous at zero. As an application, we also study the ultraweak continuity of (α, β)-derivations on von Neumann algebras.

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Cited by 10 publications
(6 citation statements)
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“…For simple experiments, we only test the discrete data in Movielens dataset without testing other data types popular in the big data environment, e.g., continuous data type [25][26][27][28][29], Boolean data type [30], and fuzzy data type [31][32][33]. In addition, we only test a single criterion (user rating) without discussing the popular cases with multiple criteria [34][35][36][37][38][39][40][41][42][43][44] and their inner linear correlations [45][46][47][48], nonlinear correlations [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66], and weights [67][68][69][70][71][72]…”
Section: Discussionmentioning
confidence: 99%
“…For simple experiments, we only test the discrete data in Movielens dataset without testing other data types popular in the big data environment, e.g., continuous data type [25][26][27][28][29], Boolean data type [30], and fuzzy data type [31][32][33]. In addition, we only test a single criterion (user rating) without discussing the popular cases with multiple criteria [34][35][36][37][38][39][40][41][42][43][44] and their inner linear correlations [45][46][47][48], nonlinear correlations [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66], and weights [67][68][69][70][71][72]…”
Section: Discussionmentioning
confidence: 99%
“…(2) In the experiment test, only one type of decision-making data (i.e., Boolean service invocation records) is considered to judge whether two users are similar neighbors. In the future, we will extend our method to accommodate the diversity of data types in the big data environment, e.g., discrete values [46][47][48][49][50][51][52], continuous values [53][54][55][56][57], fuzzy values [58], and so on.…”
Section: Further Discussionmentioning
confidence: 99%
“…2. Second, only the dimension with Boolean values is tested without considering the diversity of data types, such as the discrete data [42][43][44][45][46][47][48][49][50][51][52], fuzzy data [53][54][55], and continuous data [56][57][58][59][60][61][62][63], as well as their integration issues. 3.…”
Section: Discussionmentioning
confidence: 99%