Peelers:

Poskim discuss the use of peelers on Shabbos, and there are essentially three opinions:

A. Rav Moshe Feinstein
Rav Moshe Feinstein is cited as being lenient in allowing the use of a vegetable peeler on Shabbos since a peeler is essentially a sophisticated knife but does not aid in borer. A similar lenient view was expressed by Rav Efraim Greenblatt zt”l and Rav Ovadia Yosef.

B. Rav Nissim Karelitz
Rav Nissim Karelitz and Shabbos K’halachah rule that a peeler is a kli borer, since it is specifically made for the activity of borer. Therefore, they forbid using a peeler on Shabbos in all cases.

C. Eglei Tal
Eglei Tal distinguishes between using peelers for two different types of fruits:

1. For fruits or vegetables with an inedible peel, such as an avocado, or for fruits with an edible peel that most people do not eat, one may not use a peeler for them on Shabbos. This is because the peeler is a designated utensil for removing the peel, and thus falls under the category of borer. Removing such a peel is only permitted with a utensil not specifically designated for such an activity, such as a knife.
2. However, in the case of a fruit or vegetable with an edible peel that is in fact eaten by most people, such as an apple, one may use a peeler. Since the peel is fundamentally “food”, the rules of borer do not apply to it.

Ketzos Hashulchan and Shemiras Shabbos K’Hilchasa accept Eglei Tal’s distinction.

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Sources:

1. Testimony of Rav Reuven Feinstein shlit”a in Shabbos Kitchen f.n. Page 102. See also Divrei Chachamim page 280 where the author, Rav Chaim Aryeh Zev Ginzberg shlit”a, ate at the home of Rav Moshe for seudah shlishis and the rebbetzin used a peeler to peel carrots.
2. Rivevos Efraim 3:235, 4:94 and 5:278.
3. Chazon Ovadia (v. 4 p. 231). See also Yalkut Yosef 319:61.
4. Chut Shani (v. 2 p. 68 and 87) as well as Rav Elyashiv quoted in Shalmei Yehudah (6:(27)).
5. Rav Nissim Karelitz 13:4, with further analysis at 13n5 and 13n9. A similar strict view can be found in Shu”t Mechezeh Eliyahu 1:51,52.
6. Borer 6n12.
7. See Shemiras Shabbos K’Hilchoso 3:30, where he writes that examples of edible peels include apples, tomatoes, pears, peaches, and the skin of many fish varieties. He adds that whether a particular peel is usually eaten should be ascertained in each locality.
8. Ketzos Hashulchan 125:16. Badei Hashulchan 42. 126:3.
9. Shemiras Shabbos K’Hilchasa 3:34-35.
10. For an extended discussion of this question, especially Tzemach Tzedek’s opinion, see Piskei Dinim 319, 14d; Shabbos K’halachah Tosefes Biur 13:1; Rav Yosef Yeshaya Braun’s B’Inyan Borer B’Kiluf Peiros and B’Inyan Kiluf Perios L’Daas HaTzemach Tzedek V’Hanafka Minah L’Maaseh, printed in Kovetz Hearos Tmimim V’Anash Tzemach Tzedek vol. 1 pp. 48-66. See also Divrei Shalom 319:9.