# Category: Invariant subspaces

Krylov subspace
In linear algebra, the order-r Krylov subspace generated by an n-by-n matrix A and a vector b of dimension n is the linear subspace spanned by the images of b under the first r powers of A (starting f
Beurling factorization
No description available.
Hypercyclic operator
In mathematics, especially functional analysis, a hypercyclic operator on a Banach space X is a bounded linear operator T: X → X such that there is a vector x ∈ X such that the sequence {Tn x: n = 0,
Reflexive operator algebra
In functional analysis, a reflexive operator algebra A is an operator algebra that has enough invariant subspaces to characterize it. Formally, A is reflexive if it is equal to the algebra of bounded
Wold's decomposition
In mathematics, particularly in operator theory, Wold decomposition or Wold–von Neumann decomposition, named after Herman Wold and John von Neumann, is a classification theorem for isometric linear op
Semisimple operator
In mathematics, a linear operator T on a vector space is semisimple if every T-invariant subspace has a complementary T-invariant subspace; in other words, the vector space is a semisimple representat
Invariant subspace problem
In the field of mathematics known as functional analysis, the invariant subspace problem is a partially unresolved problem asking whether every bounded operator on a complex Banach space sends some no
Controlled invariant subspace
In control theory, a controlled invariant subspace of the state space representation of some system is a subspace such that, if the state of the system is initially in the subspace, it is possible to
Quasinormal operator
In operator theory, quasinormal operators is a class of bounded operators defined by weakening the requirements of a normal operator. Every quasinormal operator is a subnormal operator. Every quasinor
Beurling–Lax theorem
In mathematics, the Beurling–Lax theorem is a theorem due to and which characterizes the shift-invariant subspaces of the Hardy space . It states that each such space is of the form for some inner fun