• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.157-169
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• 1999

We consider the C\ulcorner-algebra O\ulcorner generated by infinite isometries \ulcorner,\ulcorner, …on Hilbert spaces with the property \ulcorner \ulcorner$\leq$1 for every n$\in$N. We present certain type of representations of C\ulcorner-algerbra O\ulcorner on a separable Hilbert space and study the conditions for irreducibility of these representations.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.365-371
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• 1999

In this paper, we prove that the range of homomorphism from a C\ulcorner-algebra A into a commutative Banach algebra B whose radical is nil contains no non-zero element of the radical of B. Using this result we show that there is no non-zero homomorphism from a C\ulcorner-algebra into a commutative radical nil Banach algebra.