Geodesic
Interpolation and Spectra of Regular LP -Space Operators
Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 470-481

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We consider the Banach algebra consisting of linear operators T which are defined on the simple functions and have bounded extensions Tp on LP for all values of p ∊ [1, ∞]. We show that the 'integral' operators in this algebra form a right ideal, and that each Tp associated to an integral T is regular. When the underlying measure is finite or special discrete we show further that every Tp is regular for every T in the algebra. Algebraic techniques together with interpolation results are then used to get relationships between the spectrum and the order spectrum of the associated Tp 's.
DOI : 10.4153/CMB-1990-076-9
Mots-clés : 47A10, 47B55 
Saxe, Karen. Interpolation and Spectra of Regular LP -Space Operators. Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 470-481. doi: 10.4153/CMB-1990-076-9
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     author = {Saxe, Karen},
     title = {Interpolation and {Spectra} of {Regular} {LP} {-Space} {Operators}},
     journal = {Canadian mathematical bulletin},
     pages = {470--481},
     year = {1990},
     volume = {33},
     number = {4},
     doi = {10.4153/CMB-1990-076-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-076-9/}
}
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