One of the uses of "of", perhaps the most important one, is to express a relationship between a part and a whole. For example, "He is a member OF that family" (member OF family) "I want a piece OF that cake" (piece OF cake) Those examples are physical, but the relationship can also be abstract. In such cases, the relation expresses membership in a category. For example, "He sang songs OF joy" (his songs belong to the category of "the joyful") "He performed acts OF mercy" (his acts belong to the category of "the merciful") "Her ability to explain is a skill OF value" (the ability belongs to the category of "the valuable").

It would be 'I hope this is valuable' (adjective). 'To be if some value' is an idiomatic phrase and therefore does not conform to grammatical logic 🙂

The word "of" in the sentence "Hope this is of some value" is used to indicate possession or relationship between the subject ("this") and the object ("some value"). In this context, "of" is used to show that the value being referred to belongs to or is associated with the thing being talked about. Without "of," the sentence would not convey the same meaning and might sound incomplete or unclear. So, while "Hope this is some value" might be grammatically correct, it does not convey the same intended meaning as "Hope this is of some value." The addition of "of" clarifies that the value being referred to belongs to or is associated with the thing being talked about. In summary, the use of "of" in this sentence is necessary to convey the intended meaning, and omitting it would change the sentence's meaning.

Hope this is OF some value is grammatically correct. Otherwise you would say, " Hope this brings some value to you." "Hope this is valuable" could also be said, but might not express humility.