Displaying similar documents to “Topological radicals, I. Basic properties, tensor products and joint quasinilpotence”

Tensor products in the category of topological vector spaces are not associative

Helge Glöckner (2004)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We show by example that the associative law does not hold for tensor products in the category of general (not necessarily locally convex) topological vector spaces. The same pathology occurs for tensor products of Hausdorff abelian topological groups.

The associated tensor norm to ( q , p ) -absolutely summing operators on C ( K ) -spaces

J. A. López Molina, Enrique A. Sánchez-Pérez (1997)

Czechoslovak Mathematical Journal

Similarity:

We give an explicit description of a tensor norm equivalent on C ( K ) ⊗ F to the associated tensor norm ν q p to the ideal of ( q , p ) -absolutely summing operators. As a consequence, we describe a tensor norm on the class of Banach spaces which is equivalent to the left projective tensor norm associated to ν q p .

Radicals of ideals that are not the intersection of radical primes

D. Laksov, M. Rosenlund (2005)

Fundamenta Mathematicae

Similarity:

Various kinds of radicals of ideals in commutative rings with identity appear in many parts of algebra and geometry, in particular in connection with the Hilbert Nullstellensatz, both in the noetherian and the non-noetherian case. All of these radicals, except the *-radicals, have the fundamental, and very useful, property that the radical of an ideal is the intersection of radical primes, that is, primes that are equal to their own radical. It is easy to verify that...