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The σ-strong topology or ultrastrong topology or strongest topology or strongest operator topology is defined by the family of seminorms p w (x) for positive elements w of B(H) *. It is stronger than all the topologies below other than the strong * topology. Warning: in spite of the name "strongest topology", it is weaker than the norm topology.)
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property.
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.
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 ...
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 .
This is a list of useful examples in general topology, a field of mathematics. Alexandrov topology; Cantor space; Co-kappa topology Cocountable topology; Cofinite topology; Compact-open topology; Compactification; Discrete topology; Double-pointed cofinite topology; Extended real number line; Finite topological space; Hawaiian earring; Hilbert cube
This topology does not depend on the neighborhood basis that was chosen and it is known as the topology of uniform convergence on the sets in or as the -topology. [2] However, this name is frequently changed according to the types of sets that make up (e.g. the "topology of uniform convergence on compact sets" or the "topology of compact ...
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 ...