1. CJM 2008 (vol 60 pp. 1010)
 Galé, José E.; Miana, Pedro J.

$H^\infty$ Functional Calculus and MikhlinType Multiplier Conditions
Let $T$ be a sectorial operator. It is known that the existence of a
bounded (suitably scaled) $H^\infty$ calculus for $T$, on every
sector containing the positive halfline, is equivalent to the
existence of a bounded functional calculus on the Besov algebra
$\Lambda_{\infty,1}^\alpha(\R^+)$. Such an algebra
includes functions defined by Mikhlintype conditions and so the
Besov calculus can be seen as a result on multipliers for $T$. In
this paper, we use fractional derivation to analyse in detail the
relationship between $\Lambda_{\infty,1}^\alpha$ and Banach algebras
of Mikhlintype. As a result, we obtain a new version of the quoted
equivalence.
Keywords:functional calculus, fractional calculus, Mikhlin multipliers, analytic semigroups, unbounded operators, quasimultipliers Categories:47A60, 47D03, 46J15, 26A33, 47L60, 47B48, 43A22 

2. CJM 2007 (vol 59 pp. 638)
 MacDonald, Gordon W.

Distance from Idempotents to Nilpotents
We give bounds on the distance from a nonzero idempotent to the
set of nilpotents in the set of $n\times n$ matrices in terms of
the norm of the idempotent. We construct explicit idempotents and
nilpotents which achieve these distances, and determine exact
distances in some special cases.
Keywords:operator, matrix, nilpotent, idempotent, projection Categories:47A15, 47D03, 15A30 

3. CJM 2005 (vol 57 pp. 506)
 Gross, Leonard; Grothaus, Martin

Reverse Hypercontractivity for Subharmonic Functions
Contractivity and hypercontractivity properties of semigroups
are now well understood when the generator, $A$, is a Dirichlet form
operator.
It has been shown that in some holomorphic function spaces the
semigroup operators, $e^{tA}$, can be bounded {\it below} from
$L^p$ to $L^q$ when $p,q$ and $t$ are suitably related.
We will show that such lower boundedness occurs also in spaces
of subharmonic functions.
Keywords:Reverse hypercontractivity, subharmonic Categories:58J35, 47D03, 47D07, 32Q99, 60J35 

4. CJM 2000 (vol 52 pp. 197)
 Radjavi, Heydar

Sublinearity and Other Spectral Conditions on a Semigroup
Subadditivity, sublinearity, submultiplicativity, and other
conditions are considered for spectra of pairs of operators on a
Hilbert space. Sublinearity, for example, is a weakening of the
wellknown property~$L$ and means $\sigma(A+\lambda B) \subseteq
\sigma(A) + \lambda \sigma(B)$ for all scalars $\lambda$. The
effect of these conditions is examined on commutativity,
reducibility, and triangularizability of multiplicative semigroups
of operators. A sample result is that sublinearity of spectra
implies simultaneous triangularizability for a semigroup of compact
operators.
Categories:47A15, 47D03, 15A30, 20A20, 47A10, 47B10 

5. CJM 1997 (vol 49 pp. 736)