The spaces and are ultrabornological. A new proof.
The Splitting Relation for Köthe Spaces.
The Steinitz theorem on rearrangement of series for nuclear spaces.
The Stieltjes moment problem in vector lattices.
The strong spectral extension property does not imply the multiplicative Hahn-Banach property
An example is given of a semisimple commutative Banach algebra that has the strong spectral extension property but fails the multiplicative Hahn-Banach property. This answers a question posed by M. J. Meyer in [4].
The Strong Topology on a Rearrangement Invariant Köthe Space.
The Strong Topology on the Dual Space of a Summability Field and the Mu-Continuity Problem.
The strongest vector space topology is locally convex on separable linear subspaces
Let X be a real or complex vector space equipped with the strongest vector space topology . Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.
The structure of Eberlein, uniformly Eberlein and Talagrand compact spaces in Σ()
The sums of closed subspaces in a topological linear space
The symmetric tensor product of a direct sum of locally convex spaces
An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective “full” tensor product of a locally convex space E are isomorphic if E is isomorphic to its square .
The Taylor spectrum and quotient Banach spaces
The tensor algebra of power series spaces
The linear isomorphism type of the tensor algebra T(E) of Fréchet spaces and, in particular, of power series spaces is studied. While for nuclear power series spaces of infinite type it is always s, the situation for finite type power series spaces is more complicated. The linear isomorphism T(s) ≅ s can be used to define a multiplication on s which makes it a Fréchet m-algebra . This may be used to give an algebra analogue to the structure theory of s, that is, characterize Fréchet m-algebras...
The tensor product of a locally pseudo-convex and a nuclear space
The theory of bounding subsets of topological vector spaces without convexity condition
The three space problem for locally bounded -spaces
The topological product structure of systems of Lebesgue spaces.
The topological proof of the Nachbin-Shirota's theorem
The Tsirelson space has a unique unconditional basis up to permutation for .
The uniform boundedness principle for order bounded operators.