\mathversion{bold}SPECTRAL CONTINUITY OF $(p,k)$-QUASIPOSINORMAL OPERATOR AND $(p,k)$-QUASIHYPONORMAL OPERATOR

Abstract

An operator T ∈ B(H) is said to be (p, k)-quasiposinormal operator, if T * k (c 2 (T * T ) p − (T T * ) p )T k ≥ 0 for a positive integer 0 < p ≤ 1, some c > 0 and a positive integer k. In this paper, we prove that, the (p, k) quasi-posinormal operator is a pole of resolvent of T * . Then we prove that if {T n } is a sequence of operators in the class (p, k) − Q and (p, k) − QP which converges in the operator norm topology to an operator T in the same class, then the functions spectrum, Weyl spectrum, Browder spectrum and essential surjectivity spectrum are continuous at T .

The Isoxazole Ring and Its N‐Oxide: A Privileged Core Structure in Neuropsychiatric Therapeutics

“…[80] Piperazine sulfonamide derivatives of isoxazolines and isoxazoles, as 5-HT 2A/C receptor antagonists, have been described as antidepressants. [81] Antidepressanta ctivity has also been noted by 3,4,5-trisubstituted isoxazolines 11 (Figure 4) incorporating alicycles (e.g.,p iperazines), carboaromatics (e.g.,p henyls) and heteroaromatics (e.g.,thiophenes). [82] The cholinergic system has long been linked to cognitive processes.T he modulation of muscarinic and nicotinic acetylcholine receptors( mAChRs and nAChRs, 12;F igure 5), present in the brain, exerts ap rofounde ffect on depression and anxi- Reviews ety.Nootropics, also known as cognition enhancers, have accordingly been developed (13 and 14; Figure 5).…”

Synthesis and in vitro antibacterial activity of novel fluoroalkyl-substituted pyrazolyl oxazolidinones

“…17 For decades, there is considerable interest in introducing fluorine-containing groups into organic molecules since the growing application of organic fluorine compounds in pharmaceuticals. 20 The synthesis of key intermediates 9 is depicted in Scheme 2. β-ethyloxyvinyl fluoroalkyl ketones 5 were prepared from ethyl vinyl ether and its derivatives with fluoroalkylacetic anhydride under base condition. 19 However, literature survey showed that the incorporation of these fluoroalkyl groups into oxazolidinones has not been studies systematically.…”

From Levulinic Acid to Biheterocycles: Synthesis of 1-[(5-Hydroxy-5-trifluoromethyl-3-substituted-4,5-dihydro-1H-pyrazol-1-yl)-3-(5-trifluoromethyl-1H-pyrazol-3-yl)propan-1-ones

“…These interesting biological activities have stimulated the search for efficient procedures with wide generality for building this ring system. [3][4][5][6] Levulinic acid (LA) is a well-known biogenic product from plant biomass. LA can be produced from D-glycopyranose of starch and cellulosic feedstocks.…”