Operators on Hilbert spaces

[1148/48%]

Subtopics

Matrix representation of operators in an orthonormal basis[136/44%]
Partial isometries[132/52%]
Commutators of operators[122/63%]
Riesz representation theorem[87/24%]
Orthogonal projectors in Hilbert space[61/54%]
Square root of a positive operator[53/45%]
Normal operators on Hilbert space[50/20%]
Hilbert-space adjoint operators[49/57%]
Cayley transform of operators[42/40%]
Neumann series[38/55%]
Positive operators and the operator order[37/30%]
Cyclic vectors and cyclic operators[36/50%]
Eigenvalues of Hermitian, skew-Hermitian and unitary operators[34/50%]
Unitary equivalence of operators[34/26%]
Unitary and isometric operators[30/40%]
Invariant and reducing subspaces of operators on Hilbert space[29/21%]
Left and right inverses of operators[28/46%]
Self-adjoint bounded operators[27/48%]
Sums, differences and products of projections[23/52%]
Compactness via the adjoint, powers and operator order[21/67%]
Frame operator and dual frames[21/100%]
Commutants of operators[17/35%]
Cartesian (Hermitian) decomposition of an operator[16/44%]
Kernel and range of the adjoint[16/38%]
Spectra of self-adjoint and positive operators[16/50%]
Isomorphisms and isometries of Hilbert spaces[15/27%]
Adjoints of integral operators[13/69%]
Diagonal and multiplication operators on Hilbert spaces[12/50%]
Topology of the set of invertible operators[12/75%]
Spectra of normal operators[11/45%]
Bounded sesquilinear forms on Hilbert spaces[10/50%]
Hellinger-Toeplitz theorem[10/60%]
Norm formulas for Hilbert-space operators[10/70%]
Invertibility criteria via lower bounds and the adjoint[8/75%]
Operators determined by their quadratic or sesquilinear forms[8/13%]
Vigier's theorem (monotone sequences of Hermitian operators)[8/38%]
Products, powers and functions of self-adjoint operators[7/57%]
Rank-one and finite-rank operators on Hilbert spaces[7/86%]
Spectrum of the Hilbert-space adjoint[7/43%]
Norm attainment by compact operators[6/67%]
Orthogonal projection onto a subspace and orthonormal systems[6/33%]
Von Neumann mean ergodic theorem[5/60%]
Matrix realizations of adjoint, self-adjoint and unitary operators[4/75%]
Operator matrices[3/100%]
Pseudoinverse of closed-range operators on Hilbert space[3/100%]
Douglas factorization (range inclusion) lemma[2/50%]
Factorization into normal operators and symmetries[2/100%]
Von Neumann alternating projection theorem[2/50%]
Pairs of Projections