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A vector v on a Hilbert space H is said to be cyclic if there exists some bounded linear operator T on H so that the set of orbits {T^iv}_(i=0)^infty={v,Tv,T^2v,...} is dense ...

A set class which is not a set.

A set of 15 open problems on Schrödinger operators proposed by mathematical physicist Barry Simon (2000). This set of problems follows up a 1984 list of open problems in ...

Definitions about a set which depend on the entire set.

Let phi:M->M be a C^1 diffeomorphism on a compact Riemannian manifold M. Then phi satisfies Axiom A if the nonwandering set Omega(phi) of phi is hyperbolic and the periodic ...

A bounded linear operator T in B(H) on a Hilbert space H is said to be cyclic if there exists some vector v in H for which the set of orbits ...

A set considered together with the sigma-algebra on the set.

For a normed space (X,||·||), define X^~ to be the set of all equivalent classes of Cauchy sequences obtained by the relation {x_n}∼{y_n} if and only if lim_(n)||x_n-y_n||=0. ...

The set closure of the set of arguments of a function f for which f is not zero.

Let H be a Hilbert space and (e_i)_(i in I) is an orthonormal basis for H. The set S(H) of all operators T for which sum_(i in I)||Te_i||^2<infty is a self-adjoint ideal of ...