Geodesic
On limits of $L_p$-norms of an integral operator
Applications of Mathematics, Tome 39 (1994) no. 4, pp. 299-307
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A recurrence relation for the computation of the $L_p$-norms of an Hermitian Fredholm integral operator is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the $L_p$-norms for the approximation of the spectral radius of this operator an a priori and an a posteriori bound for the error are obtained. Some properties of the a posteriori bound are discussed.
A recurrence relation for the computation of the $L_p$-norms of an Hermitian Fredholm integral operator is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the $L_p$-norms for the approximation of the spectral radius of this operator an a priori and an a posteriori bound for the error are obtained. Some properties of the a posteriori bound are discussed.
DOI : 10.21136/AM.1994.134259
Classification : 47A10, 47A30, 47A53, 47B15, 47G10
Keywords: $L_p$-norms of an integral operator; Hermitian Fredholm integral operator 
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Stavinoha, Pavel. On limits of $L_p$-norms of an integral operator. Applications of Mathematics, Tome 39 (1994) no. 4, pp. 299-307. doi: 10.21136/AM.1994.134259

[1] L. G. Brown, H. Kosaki: Jensen’s inequality in semi-finite von Neumann algebras. J. Operator Theory 23 (1990), 3–19. | MR

[2] A. C. Hearn: REDUCE 2 user’s manual. University of Utah, USA, 1973.

[3] R. A. Kunze: $L_p$ Fourier transforms on locally compact unimodular groups. Trans. Amer. Math. Soc. 89 (1958), 519–540. | MR

[4] C. A. McCarthy: $c_p$. Israel J. Math. 5 (1967), 249–271. | MR

[5] S. G. Michlin, Ch. L. Smolickij: Approximate methods of solution of differential and integral equations. Nauka, Moscow, 1965. (Russian) | MR

[6] J. Peetre, G. Sparr: Interpolation and non-commutative integration. Ann. of Math. Pura Appl. 104 (1975), 187–207. | DOI | MR

[7] I. E. Segal: A non-commutative extension of abstract integration. Ann. of Math. 57 (1953), 401–457, correction 58(1953), 595–596. | DOI | MR | Zbl

[8] P. Stavinoha: Convergence of $L_p$-norms of a matrix. Aplikace matematiky 30 (1985), 351–360. | MR

[9] P. Stavinoha: On limits of $L_p$-norms of a linear operator. Czech. Math. J. 32 (1982), 474–480. | MR

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