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It is stronger than the weak operator topology. The weak operator topology (WOT) or weak topology is defined by the seminorms |(x(h 1), h 2)| for h 1, h 2 ∈ H. (Warning: the weak Banach space topology, the weak operator topology, and the ultraweak topology are all sometimes called the weak topology, but they are different.)
In solid modeling and computer-aided design, the Euler operators modify the graph of connections to add or remove details of a mesh while preserving its topology. They are named by Baumgart [1] after the Euler–Poincaré characteristic. He chose a set of operators sufficient to create useful meshes, some lose information and so are not invertible.
In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators , and consideration may be given to nonlinear operators .
The weak topology on a JW algebra M is define by the seminorms |f(a)| where f is a normal state; the strong topology is defined by the seminorms |f(a 2)| 1/2. The quadratic representation and Jordan product operators L(a)b = a ∘ b are continuous operators on M for both the weak and strong topology. An idempotent p in a JBW algebra M is called ...
The ultrastrong topology is stronger than the strong operator topology. One problem with the strong operator topology is that the dual of B(H) with the strong operator topology is "too small". The ultrastrong topology fixes this problem: the dual is the full predual B * (H) of all trace class operators. In general the ultrastrong topology is ...
The predual of B(H) is the trace class operators C 1 (H), and it generates the w*-topology on B(H), called the weak-star operator topology or σ-weak topology. The weak-operator and σ-weak topologies agree on norm-bounded sets in B(H). A net {T α} ⊂ B(H) converges to T in WOT if and only Tr(T α F) converges to Tr(TF) for all finite-rank ...
The Kaplansky density theorem can be used to formulate some approximations with respect to the strong operator topology. 1) If h is a positive operator in (A −) 1, then h is in the strong-operator closure of the set of self-adjoint operators in (A +) 1, where A + denotes the set of positive operators in A. 2) If A is a C*-algebra acting on ...
The Cotlar–Stein almost orthogonality lemma is a mathematical lemma in the field of functional analysis.It may be used to obtain information on the operator norm on an operator, acting from one Hilbert space into another, when the operator can be decomposed into almost orthogonal pieces.