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...>\mathcal{L}(X,Y)</math> of [[continuous linear operator|continuous linear operators]] from ''X'' to ''Y'', then often ''strong measurability'' means that the o ==Bounded operators== ...

...operator ideal, it must contain the class of all finite-rank Banach space operators. ...ath>, denote by <math>\mathcal{J}(X,Y)</math> the set of continuous linear operators of the form <math>T:X\to Y</math> such that <math>T \in \mathcal{J}</math>. ...

...of a [[normal operator]]. More precisely, a [[bounded operator|bounded]] [[linear operator]] ''T'' on a complex [[Hilbert space]] ''H'' is said to be paranor The class of paranormal operators was introduced by V. Istratescu in 1960s, though the term "paranormal" is p ...

...r''' is a generalization of a [[normal operator]]. In general, a bounded [[linear operator]] ''T'' on a complex [[Hilbert space]] ''H'' is said to be '''''p' ...-hyponormal operators was introduced by Xia, and the class of p-hyponormal operators was studied by Aluthge, who used what is today called the [[Aluthge transfo ...

{{Short description|Theorem on linear operators}} ...matrix theory]] about the representation of a sum of two bounded, [[linear operators]] (resp. matrices). The theorem was proven by [[Theodore Motzkin]] and [[Ol ...

...oldberg|first3=Nahum|last3=Krupnik|title=Traces and Determinants of Linear Operators|series=Operator Theory Advances and Applications |publisher=Birkhäuser |pla ===⅔-nuclear operators=== ...

| title = On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space ...topic, so is not currently appropriate to link to--> of [[Hilbert space]] operators. It is generally attributed to [[Ronald G. Douglas]], although Douglas ackn ...

...dence between two-sided [[ideal (ring theory)|ideal]]s of bounded [[linear operators]] of a separable infinite-dimensional [[Hilbert space]] and Calkin sequence It originated from [[John von Neumann]]'s study of symmetric norms on [[linear algebra|matrix algebras]].<ref name="vN1">{{cite journal ...

...esolvent]] is uniformly bounded from above outside any larger sector. Such operators might be [[Unbounded operator|unbounded]]. Sectorial operators have applications in the theory of [[Elliptic partial differential equation ...

...{Cite journal|last=Aluthge|first=Ariyadasa|date=1990|title=On p-hyponormal operators for 0 < ''p'' < 1|journal=Integral Equations Operator Theory|volume=13|issu ...be a [[Hilbert space]] and let <math>B(H)</math> be the algebra of linear operators from <math>H</math> to <math>H</math>. By the [[polar decomposition]] theor ...

...not extend to the weak trace class. Instead the ideal of weak trace-class operators admits an infinite number of linearly independent quasi-continuous traces, Weak trace-class operators feature in the [[noncommutative geometry]] of French mathematician [[Alain ...

...ast=Russo |first=B. |author2=H. A. Dye |year=1966|title=A Note on Unitary Operators in C*-Algebras |journal=Duke Mathematical Journal |volume=33 |pages=413–416 A more precise result is true for the [[C*-algebra]] of all [[bounded linear operator]]s on a [[Hilbert space]]: If ''T'' is such an operator and ||''T' ...

...nch of [[mathematics]], a '''strictly singular operator''' is a [[bounded linear operator]] between normed spaces which is not bounded below on any infinite ...], and denote by ''B(X,Y)'' the space of [[bounded linear operator|bounded operators]] of the form <math>T:X\to Y</math>. Let <math>A\subseteq X</math> be any ...

...near functional operators, including linear differential and/or recurrence operators.<ref>{{Cite journal | last1 = Chyzak | first1 = Frédéric | last2 = Salvy | ...

...]] [[Yang Chen-Ning]] and [[Rodney Baxter]]. These [[mathematical operator|operators]] are particularly notable for providing solutions to the quantum [[Yang–Ba ...h>k</math>, Yang–Baxter operators are [[multilinear mapping|<math>k</math>-linear mappings]] <math>R: V \otimes_k V \rightarrow V \otimes_k V</math>. The ope ...

'''Theorem''': ''Two operators of the form are equivalent under [[gauge transformation]]s if and only if t Here the operators ...

...''' give a [[mathematical formulation of quantum mechanics]] in terms of [[linear operator|operator]]s on a [[Hilbert space]]. They were introduced by [[Paul ...alysis)|states]] of the C*-algebra (in other words the normalized positive linear functionals <math>\omega</math>). ...

{{Short description|Subset T of a topological vector space X where the linear span of T is a dense subset of X}} ...ath>X</math> is said to be a '''total''' subset of <math>X</math> if the [[linear span]] of <math>T</math> is a [[Dense set|dense subset]] of <math>X.</math> ...

...an [[eigenvalue]] of a [[Unbounded operator#Closed linear operators|closed linear operator]] is called '''normal''' if the space admits a decomposition into ...in a Banach space|root lineal]] <math>\mathfrak{L}_\lambda(A)</math> of a linear operator <math>A:\,\mathfrak{B}\to\mathfrak{B}</math> with domain <math>\ma ...

...]], [[number theory]]) and in physics. Properties of oscillatory integral operators have been studied by [[Elias M. Stein|Elias Stein]] and his school.<ref>Eli ...per on [[Fourier integral operator]]s:<ref>L. Hörmander ''Fourier integral operators'', Acta Math. '''127''' (1971), 79–183. {{doi|10.1007/BF02392052}}</ref> ...