Bashkësitë dhe operatorët e “vegjël” në Analizën Funksionale
Sets and “small” operators in functional analysis

Summary/Abstract: Each of us in daily life has come across with images that show great interest due to the perfect combination of beauty, complexity and that of infinite structure. These images are called Fractal and their visible feature that characterizes them is self-similarity, which means the one part is reminiscent of the whole. This self-similarity it can be exact, fairly accurate or statistical. Given the definition of the size of a set as “the minimum number of coordinates needed to define each point of the set”, we reach an odd conclusion to the case of Fractal: The length of a “line” that links the two ends points has infinite length and hence it follows that we cannot determine occurrence of a point in a Fractal by the oriented length because this length is infinite. How will we operate to find the size of a fractal? In this paper, based in the concepts of “smallness”, using the sets and the operators most frequently encountered in mathematical analysis, and so the measurement theory, the functional analysis and operator’s theory, we come up with a formulas to calculate the magnitude of Fractal. The analyses and the concepts used can be valuable to anyone, engineers, and economists etc. who are interest-depth studies for certain purposes.

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