Linear operators

mapping that preserves the operations of addition and scalar multiplication

congruent transformation of a geometric space that preserves at least one point

mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points

linear transformation that, when applied multiple times to any value, gives the same result as if it were applied once

linear mapping from a vector space into its field of scalars

surjective bounded operator on a Hilbert space preserving the inner product

type of continuous linear operator

linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L(v) to that of v is bounded by the same number, over all non-zero vectors v in X

(on a complex Hilbert space) continuous linear operator

densely defined operator on a Hilbert space whose domain coincides with that of its adjoint and which equals its adjoint; symmetric operator whose adjoint's domain equals its own domain

linear operator whose graph is closed

bounded operator with kernel and cokernel both having finite dimension

compact operator for which a finite trace can be defined

nuclear operator of order 2; a bounded operator A on a Hilbert space H such that tr(A*A) is finite

technique to solve differential equations

Function between topological vector spaces

homomorphism between modules, paired with the associated homomorphism between the respective base rings

linear operator defined on a dense linear subspace

compression of a multiplication operator on the circle to the Hardy space

operators on Banach spaces with properties similar to finite-dimensional operators