An example for Gelfand's theory of commutative Banach algebras
An example of a function, which is not a d.c. function
Let , . We construct a function which has Lipschitz Fréchet derivative on but is not a d.c. function.
An example of a continuum of pairwise non-isomorphic spaces of -functions
An example of a Fréchet algebra which is a principal ideal domain
We construct an example of a Fréchet m-convex algebra which is a principal ideal domain, and has the unit disk as the maximal ideal space.
An example of a maximal unimodular Dirichlet algebra.
An Example of a Non Nuclear C*-Algebra, which has the Metric Approximation Property.
An example of a nonseparable Banach algebra without nonseparable commutative subalgebras
An example of a non-topologizable algebra
We present an example of an algebra that is generated by elements, and cannot be made a topological algebra. This answers a problem posed by W. Żelazko.
An example of a normal space non-isomorphic to its product by the real line
An Example of a Nuclear Fréchet Space Without the Bounded Approximation Property.
An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices
We show that for every there exists a weight such that the Lorentz Gamma space is reflexive, its lower Boyd and Zippin indices are equal to zero and its upper Boyd and Zippin indices are equal to one. As a consequence, the Hardy-Littlewood maximal operator is unbounded on the constructed reflexive space and on its associate space .
An example of a subalgebra of on the unit disk whose stable rank is not finite
We present an example of a subalgebra with infinite stable rank in the algebra of all bounded analytic functions in the unit disk.
An example of a Ф-algebra whose uniform closure is a ring of continuous functions
An example of an irreducible subfactor of the hyperfinite II1 factor with rational, noninteger index.
An example of infinite dimensional reflexive Banach space non-isomorphic to its Cartesian square
An example of infinite dimensional reflexive space non-isomorphic to its cartesian square
An example of J. W. Roberts of a convex compact subset in a linear metric space with no extreme points
An example of semilinear topologies.
An Existence Result for Simple Inductive Limits of Interval Algebras.
An existence theorem for the Urysohn integral equation in Banach spaces