We prove that if either T or [T.sup.*] is algebraically [k.sup.*]]-paranormal, then spectral mapping theorem holds for essential approximate

point spectrum of T.

We shall call such a matrix K an H-J generalized Hausdorff matrix, and will determind the

point spectrum of H and its adjoint, H*, considered as bounded linear Operators over the [l.sup.p] spaces, for 1 [less than or equal to] p [less than or equal to] x.

We first give a short review on supermodels in quantum mechanics where the main focus will be on selfsimilar supermodels, showing a

point spectrum which consists of basic q-versions of the natural numbers.

Unique features of the program include a graphical visualization of a test before actual execution, multiple real-time test graphics displays, auotomatic program control that is dependent on test conditions, and defined turning

point spectrum sequences.

the Weyl essential approximate

point spectrum is defined by

where [[sigma].sub.P](T) is the

point spectrum, and [[sigma].sub.PF](T) is the set of eigenvalues of finite multiplicity, of T.

Other, established iron vendors are increasing their presence in the category with new, feature-filled products at both ends of the price

point spectrum, from promotional $9.99 units to irons retailing for more than $200.

"The upstairs departments have given housewares a run for the money at the high end of the price

point spectrum," said Janet Donner, vice president of sales for Signature Housewares.

Let [[sigma].sub.p](A) (resp., [[sigma].sub.a](A)) denote the

point spectrum (resp., the approximate

point spectrum) of the operator A, and let acc[sigma](A) denote the set of accumulation points of [sigma](A).

While designer had resurgence, retailers also report action at the other end of the price

point spectrum, with interest swelling in lighter fragrances.

At this

point Spectrum Curves change direction and the angle between old and the new direction is [pi]/k+1 (as we note in Section 1, the Spectrum Curve turn to the right).

Since every boundary point of [sigma](T) is in the approximate

point spectrum [pi](T), it follows that Re[[lambda]'.sub.0] is in Re[pi](T) and hence in [sigma](ReT) (by Proposition 3).