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Maximal abelian subalgebras of B(X)

Bračič J., Kuzma B.

Commentationes Mathematicae

2008

Vol. 48, [Z] 1

95-98

Let X be an infinite dimensional complex Banach space and B(X) be the Banach algebra of all bounded linear operators on X. Zelazko [1] posed the following question: Is it possible that some maximal abelian subalgebra of B(X) is finite dimensional? Interestingly, he was able to show that there does exist an infinite dimensional closed subalgebra of B(X) with all but one maximal abelian subalgebras of dimension two. The aim of this note is to give a negative answer to the original question and prove that there does not exist a finite dimensional maximal commutative subalgebra of B(X) if dimX = ∞.

The System Yb-Co-P

Budnyk S., Kuz'ma B.

Polish Journal of Chemistry

2002

Vol. 76 / nr 11

1553-1558

Phase equilibria in Yb-Co-P system have been investigated at 870 K by X-ray analysis. The existence of early known compounds Yb2Co12P7 (structure Zr2Fe12P7), YbCo5P3 (structure YCo5P3), YbCo3P2 (structure HoCo3P2), Yb6Co30P19 (own structure) and Yb5Co19P12 (structure Sc5Co19P12) has been confirmed. Atomic coordinates in structures Yb2Co12P7 (powder method RF = 0.049) and YbCo3P2 (single crystal method, RF = 0.0393) have been determined.