Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory object of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 16th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexcreated a stub for [[normal operator]] and noticed/remembered that Tim van Beek had once created the beginning of an entry [[spectral theorem]] that he ended with an empty section on the version for normal operators. If we are lucky he will come back some day and complete this, but it looks like he won't. Maybe somebody else feels inspired to work on this entry.

   created a stub for normal operator and noticed/remembered that Tim van Beek had once created the beginning of an entry spectral theorem that he ended with an empty section on the version for normal operators. If we are lucky he will come back some day and complete this, but it looks like he won’t. Maybe somebody else feels inspired to work on this entry.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeMar 16th 2011
   • (edited Mar 16th 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexAs far as the simplest spectral theorem for bounded selfadjoint operators, more precise statement (than at [[spectral theorem]]) can be found at [[zoranskoda:spectral theorem for bounded selfadjoint operators]]. As far as normal operators, I hope I can add something later, but just to mention: of course the C-star algebra definition assumes boundedness so it has a false appearance as a more general definition; unbounded normal operators should be maybe defined separately, because of the domain of the definition both of the operator and of its adjoint which are not the entire space. I may get back to this later if somebody else will not be quicker. Thanks for starting the stub!

   As far as the simplest spectral theorem for bounded selfadjoint operators, more precise statement (than at spectral theorem) can be found at spectral theorem for bounded selfadjoint operators (zoranskoda).

   As far as normal operators, I hope I can add something later, but just to mention: of course the C-star algebra definition assumes boundedness so it has a false appearance as a more general definition; unbounded normal operators should be maybe defined separately, because of the domain of the definition both of the operator and of its adjoint which are not the entire space. I may get back to this later if somebody else will not be quicker. Thanks for starting the stub!