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searching for Operator norm 32 found (121 total)

Weak operator topology (1,634 words) [view diff] exact match in snippet view article find links to article

operator norm topology. In general, the following inclusions hold: { WOT-open sets in B ( X , Y ) } ⊆ { SOT-open sets in B ( X , Y ) } ⊆ { operator-norm-open

Hausdorff–Young inequality (2,376 words) [view diff] exact match in snippet view article find links to article

and d n {\displaystyle dn} denotes counting measure. Furthermore, the operator norm of this linear map is less than or equal to one. The map which sends

Invariant convex cone (3,569 words) [view diff] exact match in snippet view article find links to article

with arbitrarily large operator norm. Precomposing g with a suitable element in G, it follows that Z = g(0) will have operator norm greater than 1. If g(W)

Weyl's inequality (1,021 words) [view diff] exact match in snippet view article find links to article

operator norm. In jargon, it says that λ k {\displaystyle \lambda _{k}} is Lipschitz-continuous on the space of Hermitian matrices with operator norm

Closed graph theorem (functional analysis) (2,719 words) [view diff] exact match in snippet view article

^{n})\to L^{p'}(\mathbb {R} ^{n})} is a well-defined bounded operator with operator norm one when 1 / p + 1 / p ′ = 1 {\displaystyle 1/p+1/p'=1} . This result

Decomposition of spectrum (functional analysis) (3,809 words) [view diff] exact match in snippet view article

h ( s ) ⋅ f ( s ) . {\displaystyle (T_{h}f)(s)=h(s)\cdot f(s).} The operator norm of T is the essential supremum of h. The essential range of h is defined

Normal operator (1,544 words) [view diff] exact match in snippet view article find links to article

then N 1 ∗ A = A N 2 ∗ {\displaystyle N_{1}^{*}A=AN_{2}^{*}} . The operator norm of a normal operator equals its numerical radius[clarification needed]

Functional analysis (2,496 words) [view diff] exact match in snippet view article find links to article

space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The theorem was first published in 1927 by Stefan Banach and Hugo Steinhaus

Strictly singular operator (1,526 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\mathcal {E}}(X,Y)} are each closed subspaces (in the operator norm) of B(X,Y), such that the classes are invariant under composition with

Reflexive operator algebra (779 words) [view diff] exact match in snippet view article find links to article

arbitrary entries, what choice of entries in the pattern gives the smallest operator norm? Every finite-dimensional reflexive algebra is hyper-reflexive. However

Earle–Hamilton fixed-point theorem (799 words) [view diff] exact match in snippet view article find links to article

Siegel generalized disk of symmetric Hilbert-Schmidt operators with operator norm less than 1. The Earle-Hamilton theorem applies equally well in this

Maximal compact subgroup (1,772 words) [view diff] exact match in snippet view article find links to article

tends to ∞ as |X| tends to ∞. In fact this norm is equivalent to the operator norm on the symmetric operators ad X and each non-zero eigenvalue occurs

Port Perry/Hoskin Aerodrome (69 words) [view diff] case mismatch in snippet view article find links to article

Aerodrome IATA: none ICAO: none TC LID: CPP3 Summary Airport type Private Operator Norm Hoskin Location Port Perry Time zone EST (UTC−05:00) • Summer (DST)

Chernoff bound (5,089 words) [view diff] exact match in snippet view article find links to article

[M_{i}]=0} . Let us denote by ‖ M ‖ {\displaystyle \lVert M\rVert } the operator norm of the matrix M {\displaystyle M} . If ‖ M i ‖ ≤ γ {\displaystyle \lVert

Hilbert C*-module (3,094 words) [view diff] exact match in snippet view article find links to article

maps L ( E , F ) {\displaystyle {\mathcal {L}}(E,F)} , normed by the operator norm. The adjointable and compact adjointable operators are subspaces of

Ergodic theory (3,727 words) [view diff] exact match in snippet view article find links to article

The ergodic means, as linear operators on Lp(X, Σ, μ) also have unit operator norm; and, as a simple consequence of the Birkhoff–Khinchin theorem, converge

Kantorovich theorem (1,474 words) [view diff] exact match in snippet view article find links to article

L\;\|\mathbf {x} -\mathbf {y} \|} holds. The norm on the left is the operator norm. In other words, for any vector v ∈ R n {\displaystyle \mathbf {v} \in

Nuclear operators between Banach spaces (1,268 words) [view diff] exact match in snippet view article find links to article

_{n}\rho _{n}f_{n}^{*}(\cdot )g_{n}} with the sum converging in the operator norm. Operators that are nuclear of order 1 are called nuclear operators:

Alternating-direction implicit method (3,498 words) [view diff] exact match in snippet view article find links to article

_{j}I)}{(M-\beta _{j}I)}}.} where ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|_{2}} is the operator norm. The ideal set of shift parameters { ( α j , β j ) } j = 1 K {\displaystyle

Sequence space (3,611 words) [view diff] exact match in snippet view article find links to article

‖ p {\displaystyle |L_{x}(y)|\leq \|x\|_{q}\,\|y\|_{p}} so that the operator norm satisfies ‖ L x ‖ ( ℓ p ) ∗ = d e f sup y ∈ ℓ p , y ≠ 0 | L x ( y )

Amenable group (3,232 words) [view diff] exact match in snippet view article find links to article

L2(G) by a symmetric probability measure on G gives an operator of operator norm 1. Johnson's cohomological condition. The Banach algebra A = L1(G) is

Symmetrizable compact operator (1,384 words) [view diff] exact match in snippet view article find links to article

HS. As Krein (1947) and Reid (1951) noted, the operator has the same operator norm as K. In fact the self-adjointness condition implies S K n = ( K ∗ )

Ergodic flow (5,093 words) [view diff] exact match in snippet view article find links to article

continuously in operator norm on r on (0,1]; from the above σt(ar) is norm continuous in t. Let B0 the closure in the operator norm of the unital *-algebra

2003 Ontario general election (7,042 words) [view diff] case mismatch in snippet view article find links to article

during the Progressive Conservative leadership campaign by racetrack operator Norm Picov and the companies he owns. Mackie, Richard (October 3, 2002).

Min-entropy (2,716 words) [view diff] exact match in snippet view article find links to article

H_{\rm {min}}(\rho )=-\log \|\rho \|_{\rm {op}},} remembering that the operator norm of a Hermitian positive semidefinite operator equals its largest eigenvalue

NLTS conjecture (1,115 words) [view diff] exact match in snippet view article find links to article

Hm(n) acts non-trivially on O(1) qubits. Another constraint is the operator norm of Hm(n) is bounded by a constant independent of n and each qubit is

Inverse function theorem (7,930 words) [view diff] exact match in snippet view article find links to article

{\displaystyle |h|/2\leq |k|} . Writing ‖ ⋅ ‖ {\displaystyle \|\cdot \|} for the operator norm, | g ( y + k ) − g ( y ) − A − 1 k | = | h − A − 1 ( f ( x + h ) − f

Zonal spherical function (6,698 words) [view diff] exact match in snippet view article find links to article

A(K\G/K). The restriction of a * homomorphism χ continuous for the operator norm is also continuous for the norm ||·||1. Since the Banach space dual

Differential forms on a Riemann surface (11,073 words) [view diff] exact match in snippet view article find links to article

linear operator with operator norm ||m(φ)|| ≤ ||φ||∞. It extends continuously to a bounded linear operator on H with the same operator norm. For every open

Beltrami equation (10,901 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \displaystyle {f_{z}-g_{z}=T(\mu (f_{z}-g_{z})).}} Since Tμ has operator norm on Lp less than 1, this forces f z = g z . {\displaystyle \displaystyle

Plancherel theorem for spherical functions (11,769 words) [view diff] exact match in snippet view article find links to article

commutative. The closure of its (the Hecke algebra's) image in the operator norm is a non-unital commutative C* algebra A {\displaystyle {\mathfrak {A}}}

Mutation (Jordan algebra) (15,817 words) [view diff] exact match in snippet view article

||a|| = sup αi and is independent of choices. Its square equals the operator norm of Qτ(a). Thus V becomes a complex normed space with open unit ball