the operator norm measures the "size" of certain linear operators by assigning each a real number called its operator norm. Formally, it is a norm defined...

standard basis, and one defines the corresponding induced norm or operator norm or subordinate norm on the space K m × n {\displaystyle K^{m\times n}} of...

M} is called the operator norm of L {\displaystyle L} and denoted by ‖ L ‖ . {\displaystyle \|L\|.} A linear operator between normed spaces is continuous...

norm). The set of Hilbert–Schmidt operators is closed in the norm topology if, and only if, H is finite-dimensional. Every Hilbert–Schmidt operator T :...

the Ky Fan n-norm). The Schatten 2-norm is the Frobenius norm. The Schatten ∞-norm is the spectral norm (also known as the operator norm, or the largest...

In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance...

closure of finite-rank operators (representable by finite-dimensional matrices) in the topology induced by the operator norm. As such, results from matrix...

one can say that the weak-operator and σ-weak topologies agree on norm-bounded sets in B(H): Every trace-class operator is of the form S = ∑ i λ i u...

operator norm? Every finite-dimensional reflexive algebra is hyper-reflexive. However, there are examples of infinite-dimensional reflexive operator algebras...

reference to algebras of operators on a separable Hilbert space, endowed with the operator norm topology. In the case of operators on a Hilbert space, the...

If ‖ T n − T ‖ → 0 {\displaystyle \|T_{n}-T\|\to 0} , that is, the operator norm of T n − T {\displaystyle T_{n}-T} (the supremum of ‖ T n x − T x ‖...

logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm. The logarithmic...

the question arises what Euclidean norms the output can assume. This can be bounded by the help of the operator norm. ∀ x   ‖ P ⋅ x ‖ 2 ∈ [ ‖ P − 1 ‖ 2...

) In this case, its operator norm is equal to ‖ f ‖ ∞ {\displaystyle \|f\|_{\infty }} . The adjoint of a multiplication operator T f {\displaystyle T_{f}}...

Theorems 1 and 2 below.) The dual norm is a special case of the operator norm defined for each (bounded) linear map between normed vector spaces. Since the ground...

mathematics, a compact operator is a linear operator T : X → Y {\displaystyle T:X\to Y} , where X , Y {\displaystyle X,Y} are normed vector spaces, with...

linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. An operator between two normed spaces...

inequality for integral operators, is a bound on the L p → L q {\displaystyle L^{p}\to L^{q}} operator norm of an integral operator in terms of L r {\displaystyle...

every x in U. Bounded operators form a vector space. On this vector space we can introduce a norm that is compatible with the norms of U and V: ‖ A ⁡ ‖...

operator 2-norm. One can easily verify the relationship between the Ky Fan 1-norm and singular values. It is true in general, for a bounded operator ⁠...

is a bounded linear operator on the normed vector space X {\displaystyle X} . If the Neumann series converges in the operator norm, then I − T {\displaystyle...

transpose, of an operator A : E → F {\displaystyle A:E\to F} , where E , F {\displaystyle E,F} are Banach spaces with corresponding norms ‖ ⋅ ‖ E , ‖ ⋅ ‖...

spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue...

linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The...

creating a unit vector localized outside the region requires operators of ever increasing operator norm. This theorem is also cited in connection with quantum...

\|T\|_{1}:=\operatorname {Tr} (|T|).} One can show that the trace-norm is a norm on the space of all trace class operators B 1 ( H ) {\displaystyle B_{1}(H)} and that B 1...

[1,2]} . Furthermore, the operator norm of this linear map is less than or equal to one. Here we use the language of normed vector spaces and bounded...

formula, also holds for bounded linear operators: letting ‖ ⋅ ‖ {\displaystyle \|\cdot \|} denote the operator norm, we have ρ ( A ) = lim k → ∞ ‖ A k ‖...

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

In operator theory, a bounded operator T: X → Y between normed vector spaces X and Y is said to be a contraction if its operator norm ||T || ≤ 1. This...