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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$\mathcal L$

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / 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
Kang, Joo-Ho
Jo,, Y. , & Kang,, J. (2004). Skew-Adjoint Interpolation on $Ax=y$ in Alg$\mathcal L$, 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>

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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