#### Alladi Ramakrishnan Hall

#### Helton-Howe and Krein's Trace Formulas

#### Prof. K. B. Sinha

##### JNCASR

*Krein's formula gives an expression for the trace of the difference of a function of a self-adjoint operator and its perturbation by*

the addition of a trace-class operator , while that due to Helto and Howe deals with the trace of the commutator of functions of a hyponormal

operator and it's adjoint . The impact of Krein's theorem on the derivation of the Helton-Howe formula will be discussed .

Krein's formula gives an expression for the trace of the difference of a function of a self-adjoint operator and its perturbation by

the addition of a trace-class operator , while that due to Helto and Howe deals with the trace of the commutator of functions of a hyponormal

operator and it's adjoint . The impact of Krein's theorem on the derivation of the Helton-Howe formula will be discussed .

Krein's formula gives an expression for the trace of the difference of a function of a self-adjoint operator and its perturbation by

the addition of a trace-class operator , while that due to Helto and Howe deals with the trace of the commutator of functions of a hyponormal

operator and it's adjoint . The impact of Krein's theorem on the derivation of the Helton-Howe formula will be discussed .

Done