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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.11 No.1

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Skew-Adjoint Interpolation on $Ax=y$ in Alg$\mathcal L$

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2004, v.11 no.1, pp.29-36
Jo, Young-Soo
Kang, Joo-Ho
Jo,, Y. , & Kang,, J. (2004). Skew-Adjoint Interpolation on $Ax=y$ in Alg$\mathcal L$. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 11(1), 29-36.

Abstract

Given vectors x and ｙ in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. In this paper the following is proved: Let <TEX>$\cal{L}$</TEX> be a subspace lattice on a Hilbert space <TEX>$\cal{H}$</TEX>. Let x and ｙ be vectors in <TEX>$\cal{H}$</TEX> and let <TEX>$P_x$</TEX>, be the projection onto sp(x). If <TEX>$P_xE=EP_x$</TEX> for each <TEX>$ E \in \cal{L}$</TEX> then the following are equivalent. (1) There exists an operator A in Alg(equation omitted) such that Ax=y, Af = 0 for all f in (<TEX>$sp(x)^\perp$</TEX>) and <TEX>$A=-A^\ast$</TEX>. (2) (equation omitted)

keywords
interpolation problem, subspace lattice, skew-adjoint interpolation problem, <tex> $ALG\mathcal{L}$</tex>

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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