Funktionalanalysis

The flashcards below were created by user BloodyMary0 on FreezingBlue Flashcards.

  1. 2.Def - Stetigkeit
    chart?chf=bg,s,00000000&cht=tx&chl=T%5C%2C%20stetig%5C%20%3A%5CLongleftright%20%5Bx_n%20%5Cright%20x%20%5CRight%20Tx_n%20%5Cright%20Tx%5D&chs=556x40
  2. 2.Def - Isometrisch
    chart?chf=bg,s,00000000&cht=tx&chl=T%20%5Cin%20%5Cmathcal%7BL%7D(E%2CF)&chs=172x38 : chart?chf=bg,s,00000000&cht=tx&chl=%7C%7CTx%7C%7C%20%3D%20%7C%7Cx%7C%7C&chs=162x40 chart?chf=bg,s,00000000&cht=tx&chl=%5Cforall%20x%20%5Cin%20E&chs=114x30
  3. 2.Def - Isomorph
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cexists%20T%20%5Cin%20%5Cmathcal%7BL%7D(E%2CF)&chs=196x38 : T inv. (E chart?chf=bg,s,00000000&cht=tx&chl=%5Csimeq&chs=26x20 F)
  4. 2.Def - Invertierbar
    chart?chf=bg,s,00000000&cht=tx&chl=T%20%5Cin%20%5Cmathcal%7BL%7D(E%2CF)&chs=172x38 : T bij. & chart?chf=bg,s,00000000&cht=tx&chl=T%5E%7B-1%7D&chs=58x34 stetig.
  5. 2.Def - Operatornorm
    chart?chf=bg,s,00000000&cht=tx&chl=%7C%7C%20T%20%7C%7C%20%3D%20%5Cinf%20%5C%7B%20c%5C%2C%20%3E%5C%2C%200%20%5C%2C%7C%5C%2C%20%7C%7CTx%7C%7C%20%5Cleq%20c%20%7C%7Cx%7C%7C%5C%2C%20%5Cforall%20x%20%5Cin%20E%20%5C%7D&chs=570x42
  6. 2.Def - Operator
    • T linear & stetig.
    • chart?chf=bg,s,00000000&cht=tx&chl=T%20%5Cin%20%5Cmathcal%7BL%7D(E%2CF)&chs=172x38
  7. 3.Def - Dualraum
    chart?chf=bg,s,00000000&cht=tx&chl=T%5C%2C%20stetig%5C%20%3A%5CLongleftright%20%5Bx_n%20%5Cright%20x%20%5CRight%20Tx_n%20%5Cright%20Tx%5D&chs=556x40
  8. 3.Def - chart?chf=bg,s,00000000&cht=tx&chl=l%5Ep%20%5Cmathrm%7B-%20Raum%7D&chs=156x36
    chart?chf=bg,s,00000000&cht=tx&chl=l%5Ep%20%3D%20%5C%7B%20(x_n)_%7Bn%5Cin%20%5Cmathbb%7BN%7D%7D%5C%20%7C%5C%20%7C%7Cx%7C%7C_p%20%3D%20%5C(%5Csum_%7Bn%20%3D%200%7D%5E%5Cinfty%20%7Cx_n%7C%5Ep%5C)%20%3C%20%5C%20%5Cinfty%20%5C%7D&chs=644x58
  9. 4.Def - Äquivalente Normen
    chart?chf=bg,s,00000000&cht=tx&chl=%7C%7Cx%7C%7C_1%20%5Csim%20%7C%7Cx%7C%7C_2%20%5C%20%5CLeftright%5C%20%5Cexists%20%5Calpha%2C%20%5Cbeta%5C%20%3A%5C%20%5Calpha%7C%7Cx%7C%7C_1%20%5Cleq%20%7C%7Cx%7C%7C_2%20%5Cleq%20%5Cbeta%7C%7Cx%7C%7C_1%20%5Cforall%20x%20&chs=748x46
  10. 4.Def - Trennt Punkte
    chart?chf=bg,s,00000000&cht=tx&chl=F%20%5Csubset%20C(K)%5C%20%5Cmathrm%7Btrennt%5C%20Punkte%7D%20%5CLeftright%20%5Cforall%20x%2Cy%20%5Cin%20K%2C%20%5C%20x%20%5Cneq%20y%20%5Cexists%20f%20%5Cin%20F%20%5C%20%3A%20%5C%20f(x)%20%5Cneq%20f(y)&chs=970x48
  11. 5.Def - Gleichstetigkeit
    • chart?chf=bg,s,00000000&cht=tx&chl=(M_1%2C%5C%20d)%2C%5C%20(M_2%2C%5C%20d)%5C%20%5Cmathrm%7Bmetr.%7D%2C%5C%20A%20%5Csubset%20Abb(M_1%2CM_2)&chs=592x38
    • A gleichstetig in chart?chf=bg,s,00000000&cht=tx&chl=x_0&chs=36x28, falls
    • chart?chf=bg,s,00000000&cht=tx&chl=%5Cforall%20%5Cepsilon%5C%20%3E%5C%200%20%5Cexists%20U_%7Bx_o%7D%5C%20%3A%5C%20d(f(x)%2C%5C%20f(x_0))%20%3C%20%5Cepsilon%20%5Cforall%20f%20%5Cin%20A%2C%5C%20x%20%5Cin%20U_%7Bx_0%7D&chs=698x40
  12. 5.Def - Separabel
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cexists%20A%20%5Csubset%20E%20%5C%20%3A%20%5C%20%5Coverline%20A%20%3D%20E%20%5C%20%26%20%5C%20A%20%5C%20%5Cmathrm%7Babz.%7D&chs=388x42
  13. 6.Def - Unterverband
    • chart?chf=bg,s,00000000&cht=tx&chl=F%20%5Csubset%20C(K)%20%5C%20%5Cmathrm%7BUnterverband%7D%20%5CLeftright&chs=414x38
    • F UR & chart?chf=bg,s,00000000&cht=tx&chl=%5Bf%20%5Cin%20F%20%5CRight%20%7Cf%7C%20%5Cin%20F%5D&chs=256x40
  14. 7.Def - Skalarprodukt
    • chart?chf=bg,s,00000000&cht=tx&chl=E%5Ctimes%20E%20%5Cright%20%5Cmathbb%7BK%7D%2C%5C%20(x%2Cy)%20%5Cmapsto%20(x%7Cy)&chs=378x40 mit
    • chart?chf=bg,s,00000000&cht=tx&chl=(x%20%2B%20y%7Cz)%20%3D%20(x%7Cz)%20%2B%20(y%7Cz)&chs=368x40
    • chart?chf=bg,s,00000000&cht=tx&chl=(%5Clambda%20x%7Cy)%20%3D%20%5Clambda(x%7Cy)&chs=246x40
    • chart?chf=bg,s,00000000&cht=tx&chl=(x%7Cy)%20%3D%20%5Coverline%20%7B(y%7Cx)%7D&chs=208x50
  15. 7.Def - Prähilbertraum
    chart?chf=bg,s,00000000&cht=tx&chl=(E%2C%5C%20(%5Ccdot%5C%2C%20%7C%5C%2C%20%5Ccdot))&chs=142x40
  16. 7.Def - Hilbertraum
    Vollständiger Prähilbertraum
  17. 7.Def - Orthogonal
    chart?chf=bg,s,00000000&cht=tx&chl=x%2Cy%20%5Cin%20E%2C%5C%20x%5Cperp%20y%20%5C%20%3A%5CLeftright%20(x%7Cy)%20%3D%200&chs=410x40
  18. 8.Def -
Author:
BloodyMary0
ID:
315896
Card Set:
Funktionalanalysis
Updated:
2016-02-14 15:58:54
Tags:
Definition
Folders:

Description:
Definitionen
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