In this article, we derive some necessary and sufficient conditions for the product of hypo-EP operators to be hypo-EP and we characterize hypo-EP operators through factorizations.

The concepts and theories of consumer purchase behaviour have drawn upon various areas such as  social psychology,sociology,psychology,economics and cultural anthropology.Shopping is the examining of goods or services from retailers with the objective of purchase at that time. Different people have different perceptions while they go for shopping. Some just love to shop and think that’s the best thing to do, which gives them happiness also. Some just do shopping just to get the necessary items that are their daily use items and don’t find shopping that much fun. Shopping motivation can be described as consumer’s wants and needs as they communicate with the outlets at which to make a purchase.Store resonance is the ultimate relationship between a store and a customer. The proximity of that bond between the store and the customer can be made preciseby using four factors: loyalty, emotional bond, being a member of the store community and active store involvement.This paper aims at store resonance and shopping motives that has an influence over the gender differences of the shoppers and to study the relationship between the store resonance and shopping motives that influence the purchase behaviour of the shoppers. It is identified thatthere is a significant difference between the shopping motivation and store resonance at 1 percent and 5 percent level. Thus it is concluded that with the increase in the store resonance shopping motivation is also increased.

Fuglede-Putnam theorem is not true in general for EP operators on Hilbert spaces. We prove that under some conditions the theorem holds good. If the adjoint operation is replaced by Moore-Penrose inverse in the theorem, we get Fuglede-Putnam type theorem for EP operators -however proofs are totally different. Finally, interesting results on EP operators have been proved using several versions of Fuglede-Putnam type theorems for EP operators on Hilbert spaces.

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Fuglede-Putnam theorem is not true in general for EP operators on Hilbert spaces. We prove that under some conditions the theorem holds good. If the adjoint operation is replaced by Moore-Penrose inverse in the theorem, we get Fuglede-Putnam type theorem for EP operators -however proofs are totally different. Finally, interesting results on EP operators have been proved using several versions of Fuglede-Putnam type theorems for EP operators on Hilbert spaces.