The p-Class in a Dual B ∗ -Algebra

On certain subalgebras of a dual B*-algebra

“…Let b be a nonzero normal element in A and {e T } a maximal orthogonal family of hermitian minimal idempotents in A such that e T b = be., = k T e T , where k T is a constant. Then it is shown in Wong (1974), that the set {k n } = {k T : k T^0 } is countable and independent of the choice of {e r } and For a = 0, we define | a | p = 0 (0 < p S =°). Let A p = {a G A : | a | p < oc} (0 < p g oo).…”

“…It was shown in Wong (1974) that for l S p g^ A p is a dual A *-a!gebra which is a dense two-sided ideal of A, A = A* and A, = {a6: a, b G A 2 }. Let b,ce.A 2 and {/ T } a maximal orthogonal family of hermitian minimal idempotents in A.…”

“…The class C p (0 < p ^ oo) of compact operators in LC(H) has many interesting properties and has been studied in various articles (e.g., see Gohberg and Krein (1969) and McCarthy (1967)). In Wong (1974), a similar class of spaces A p ( 0 < p g a=) in an arbitrary dual B "-algebra A was introduced and studied. The purpose of this paper is to establish three more results for A p .…”

Algebraic difference between 𝑝-classes of an H*-algebra

“…These spaces can be considered as common generalizations of p-classes of compact operators and l p spaces (cf. [9,11,21,22]). This difference exists in spite of the fact that the methods for constructing them are rather the same.…”

“…After this we defined C p (A), the p-class of A, in a way very similar to that which is commonly done concerning the von Neumann-Schatten p-class of compact operators (cf. [21,22]). To obtain the mentioned ismorphisms between these p-classes and certain operator ideals we need the following construction.…”