## Indiana University Mathematics Journal, Volume 24, Issues 7-12 |

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Page 779

An operator T is called essentially

This condition is easily seen to be equivalent to the requirement that the image of

T in the Calkin algebra be

...

An operator T is called essentially

**unitary**if 1 — T*T and 1 — TT* are compact.This condition is easily seen to be equivalent to the requirement that the image of

T in the Calkin algebra be

**unitary**. We summarize some of the foregoing and add...

Page 780

we now see that U0 is

see e.g. [3], p. 166-167), we have U0 - T = f/„(l - P) = f/0(l + P)-\l - T*T), and thus

compactness of 1 — T*T implies compactness of U0 — T. We will show that U0 ...

we now see that U0 is

**unitary**on X and P is invertible. By a standard calculation (see e.g. [3], p. 166-167), we have U0 - T = f/„(l - P) = f/0(l + P)-\l - T*T), and thus

compactness of 1 — T*T implies compactness of U0 — T. We will show that U0 ...

Page 882

Since the last two terms tend to 0 as n — » oo , we see that Sk*A Tk = A, and

since Sh is

decomposition for A, then W is

Since the last two terms tend to 0 as n — » oo , we see that Sk*A Tk = A, and

since Sh is

**unitary**, AT* = ShA. As in [10; p. 71], if A = W(A*A)U2 is the polardecomposition for A, then W is

**unitary**and WTk = ShW for every h in g, that is, ...### What people are saying - Write a review

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### Contents

BRUCE LUND Analytic embeddings in logmodular algebras | 1093 |

RENfi RUCHTI Cohomology of forms with values in a graded Lie algebra | 1099 |

ANDREW MAJDA Disappearing solutions for the dissipative wave | 1119 |

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