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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.11 No.1

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SKEW-ADJOINT INTERPOLATION ON Ax-y IN $ALG\mathcal{L}$

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

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2004, v.11 no.1, pp.29-36
Jo, Young-Soo (Department of Mathematics, Keimyung University)
Kang, Joo-Ho (Department of Mathematics, Daegu University)
Jo, Young-Soo, & Kang, Joo-Ho. (2004). SKEW-ADJOINT INTERPOLATION ON Ax-y IN <TEX>$ALG\mathcal{L}$</TEX>, 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 $\cal{L}$ be a subspace lattice on a Hilbert space $\cal{H}$. Let x and ｙ be vectors in $\cal{H}$ and let $P_x$, be the projection onto sp(x). If $P_xE=EP_x$ for each $ E \in \cal{L}$ 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 ($sp(x)^\perp$) and $A=-A^\ast$. (2) (equation omitted)

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

한국수학교육학회지시리즈B:순수및응용수학

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