On a class of double sequence transformations
We investigate conditions under which the projective and the injective topologies coincide on the tensor product of two Köthe echelon or coechelon spaces. A major tool in the proof is the characterization of the επ-continuity of the tensor product of two diagonal operators from to . Several sharp forms of this result are also included.
We study in terms of corresponding Köthe matrices when every continuous linear operator between two Köthe spaces is bounded, the consequences of the existence of unbounded continuous linear operators, and related topics.
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