Indicwiki: 1 revision imported from :alpha:Template:Spectral_theory

2023-04-29T06:11:10Z

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alpha>Indicwiki: Created page with "{{Navbox | name = Spectral theory | title = Spectral theory and ^-algebras | state = {{{state|uncollapsed expanded
2023-03-01T08:04:35Z

Created page with "{{Navbox | name = Spectral theory | title = Spectral theory and <sup></sup>-algebras | state = {{{state|<noinclude>uncollapsed expanded</noinclude><includeo..."

New page
{{Navbox
| name = Spectral theory
| title = [[Spectral theory]] and [[-algebra|<sup></sup>-algebras]]
| state = {{{state|<noinclude>uncollapsed expanded</noinclude><includeonly>autocollapse</includeonly>}}}

| image =
| bodyclass = hlist
| selected = {{{1}}}
| above =

| group1 = Basic concepts
| list1 =
* [[-algebra|Involution/-algebra]]
* [[Banach algebra]]
* [[Banach -algebra|B-algebra]]
* [[C-algebra]]
[[Noncommutative topology]]
* [[Projection-valued measure]]
* [[Spectrum (functional analysis)|Spectrum]]
* [[Spectrum of a C-algebra]]
[[Spectral radius]]
* [[Operator space]]

| group10 = Main results
| list10 =
* [[Gelfand–Mazur theorem]]
* [[Gelfand–Naimark theorem]]
* [[Gelfand representation]]
* [[Polar decomposition]]
* [[Singular value decomposition]]
* [[Spectral theorem]]
* [[Spectral theory of normal C-algebras]]

| group15 = Special Elements/Operators
| list15 =
[[Isospectral]]
* [[Normal element|Normal]] [[Normal operator|operator]]
* [[Self-adjoint|Hermitian/Self-adjoint]] [[Self-adjoint operator|operator]]
* [[Unitary element|Unitary]] [[Unitary operator|operator]]
* [[Unit (ring theory)|Unit]]

| group20 = [[Spectrum (functional analysis)|Spectrum]]
| list20 =
* [[Krein–Rutman theorem]]
* [[Normal eigenvalue]]
* [[Spectrum of a C-algebra]]
[[Spectral radius]]
* [[Spectral asymmetry]]
* [[Spectral gap]]

| group30 = Decomposition
| list30 =
* [[Decomposition of spectrum (functional analysis)|Decomposition of a spectrum]]
[[Continuous spectrum (functional analysis)|Continuous]]
[[Point spectrum|Point]]
** [[Spectrum (functional analysis)#Residual spectrum|Residual]]
* [[Spectrum (functional analysis)#Approximate point spectrum|Approximate point]]
* [[Spectrum (functional analysis)#Compression spectrum|Compression]]
* [[Direct integral]]
* [[Discrete spectrum (mathematics)|Discrete]]
* [[Spectral abscissa]]

| group40 = Spectral Theorem
| list40 =
* [[Borel functional calculus]]
* [[Min-max theorem]]
* [[Positive operator-valued measure]]
* [[Projection-valued measure]]
* [[Riesz projector]]
* [[Rigged Hilbert space]]
* [[Spectral theorem]]
* [[Spectral theory of compact operators]]
* [[Spectral theory of normal C-algebras]]

| group52 = Special algebras
| list52 =
[[Amenable Banach algebra]]
* With an [[Approximate identity]]
* [[Banach function algebra]]
* [[Disk algebra]]
* [[Nuclear C-algebra]]
[[Uniform algebra]]
* [[Von Neumann algebra]]
** [[Tomita–Takesaki theory]]

| group55 = Finite-Dimensional
| list55 =
* [[Alon–Boppana bound]]
* [[Bauer–Fike theorem]]
* [[Numerical range]]
* [[Schur–Horn theorem]]

| group65 = Generalizations
| list65 =
* [[Dirac spectrum]]
* [[Essential spectrum]]
* [[Pseudospectrum]]
* [[Structure space]] ([[Shilov boundary]])

| group70 = Miscellaneous
| list70 =
* [[Abstract index group]]
* [[Banach algebra cohomology]]
* [[Cohen–Hewitt factorization theorem]]
* [[Extensions of symmetric operators]]
* [[Fredholm theory]]
* [[Limiting absorption principle]]
* [[Schröder–Bernstein theorems for operator algebras]]
* [[Sherman–Takeda theorem]]
* [[Unbounded operator]]

| group85 = Examples
| list85 =
* [[Wiener algebra]]

| group90 = Applications
| list90 =
* [[Almost Mathieu operator]]
* [[Corona theorem]]
* [[Hearing the shape of a drum]] ([[Dirichlet eigenvalue]])
* [[Heat kernel]]
* [[Kuznetsov trace formula]]
* [[Lax pair]]
* [[Proto-value function]]
* [[Ramanujan graph]]
* [[Rayleigh–Faber–Krahn inequality]]
* [[Spectral geometry]]
* [[Spectral method]]
* [[Spectral theory of ordinary differential equations]]
* [[Sturm–Liouville theory]]
* [[Superstrong approximation]]
* [[Transfer operator]]
* [[Transform theory]]
* [[Weyl law]]
* [[Wiener–Khinchin theorem]]

}}
<noinclude>
{{Documentation
| content =
{{Collapsible option |statename=optional}}
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[[Category:Mathematics navigational boxes]]
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